SEARCH
Search Details
Inoguchi Junichi
| Faculty of Science Mathematics Mathematics | Professor |
| Research Center of Mathematics for Social Creativity | Professor |
Researcher basic information
■ Degree■ URL
researchmap URLホームページURL■ Various IDs
Researcher number
- 40309886
Research Keyword
- harmonic map
- Integrable Systems
- loop group
- AdS/CFT
- magnetic trajectory
- CMC surface
- DPW-method
- contact structure
- spin structure
- minimal surface
- magnetic harmonic map
- Locally conformal Kaehler manifold
- Vaisman manifold
- Differential Geometry
- Discrete Differential Geometry
- Bachelor's degree program, School of Science
- Master's degree program, Graduate School of Science
- Doctoral (PhD) degree program, Graduate School of Science
Research activity information
■ Papers- Holomorphic statistical 2-manifolds and almost contact statistical 3-manifolds
Jun-ichi Inoguchi
Differential Geometry and its Applications, 103, 102366, 102366, Elsevier BV, Jun. 2026, [Peer-reviewed], [International Magazine]
English, Scientific journal - Biharmonic hypersurfaces in projective spaces revisited
Jun-ichi Inoguchi; Toru Sasahara
International Electronic Journal of Geometry, 18, 2, 293, 334, International Electronic Journal of Geometry, Person (Kazim ILARSLAN), 19 Oct. 2025, [Peer-reviewed], [Lead author, Corresponding author], [International Magazine]
English, Scientific journal, We study biharmonic homogeneous real hypersurfaces in complex projective space and quaternion projective space. We provide a classification of biharmonic homogeneous real hypersurfaces in quaternion projective space. We also classify pseudo-harmonic, subelliptic biharmonic, and Levi-harmonic homogeneous Hopf hypersurfaces in complex space forms. - Homogeneity of magnetic trajectories in the Berger sphere
Jun-ichi Inoguchi; Marian Ioan Munteanu
Journal of Mathematical Analysis and Applications, 550, 2, 129554, 129554, Elsevier BV, 15 Oct. 2025, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Grassmann geometry on $H^2\times\mathbb{R}$
Jun-ichi Inoguchi; Hiroo Naitoh
Hokkaido Mathematical Journal, 54, 3, 459, 514, Department of Mathematics, Hokkaido University, 01 Oct. 2025, [Peer-reviewed], [Lead author]
English, Scientific journal - Homogeneous statistical manifolds
Jun-ichi Inoguchi; Yu Ohno
Information Geometry, 8, 2, 285, 341, Springer Science and Business Media LLC, 09 Sep. 2025, [Peer-reviewed], [Lead author], [International Magazine]
English, Scientific journal - Codazzi and totally umbilical hypersurfaces in $\mathrm {Sol}_1^4$
Zlatko Erjavec; Jun-ichi Inoguchi
Glasgow Mathematical Journal, 67, 3, 487, 493, Sep. 2025, [Peer-reviewed], [Last author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Remarks on Ricci tensor fields of contact metric manifolds
Jun-ichi Inoguchi; Kazuhiro Okumura
Journal of Geometry, 116, 2, Springer Science and Business Media LLC, 15 Jul. 2025, [Peer-reviewed], [Lead author], [International Magazine]
English, Scientific journal - Minimal submanifolds in $\mathbb {H}^3\times \mathbb {E}^1$
Zlatko Erjavec; Jun-ichi Inoguchi
Periodica Mathematica Hungarica, 90, 2, 307, 342, Springer Science and Business Media LLC, Jun. 2025, [Peer-reviewed], [Last author], [International Magazine]
English, Scientific journal - On metrics and linear connections on lines
Jun-ichi Inoguchi
International Electronic Journal of Geometry,, 18, 1, 60, 85, 24 Apr. 2025, [Peer-reviewed], [International Magazine]
English, Scientific journal, We discuss linear connections and conformal Riemannian metricson the real line. - Catenaries, cycloids and warped products
Jun-ichi Inoguchi
International Electronic Journal of Geometry, 18, 1, 33, 47, 24 Apr. 2025, [Peer-reviewed], [International Magazine]
English, Scientific journal, We study warped products derived from catenaries and cycloids. We give an example of non-homogeneous semi-symmetric 3-space closely related to cycloids. - Homogeneous structures of 3-dimensional Sasakian space forms
Inoguchi, Jun-ichi; Ohno, Yu
Tsukuba Journal of Mathematics, 48, 2, 205, 247, 14 Mar. 2025, [Peer-reviewed], [Lead author, Corresponding author], [Domestic magazines]
English, Scientific journal - Magnetic trajectories in Walker 3-manifolds
Zlatko Erjavec; Jun-ichi Inoguchi
Journal of Mathematical Analysis and Applications, 542, 2, 128806, Elsevier BV, 15 Feb. 2025, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - On the characteristic Jacobi operator of the unit tangent sphere bundles over surfaces
Jun-ichi Inoguchi; Ji-Eun Lee
Bulletin of the Korean Mathematical Society, 61, 6, 1549, 1563, 30 Nov. 2024, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Homogeneous Riemannian structures in Thurston geometries and contact Riemannian geometries
Jun-ichi Inoguchi
International Electronic Journal of Geometry, 17, 2, 559, 659, International Electronic Journal of Geometry, Person (Kazim ILARSLAN), 27 Oct. 2024, [Peer-reviewed], [International Magazine]
English, Scientific journal,We give explicit parametrizations for all the
homogeneous Riemannian structures on model spaces of Thurston geometry.
As an application, we give all the homogeneous contact metric structures
on $3$-dimensional Sasakian space forms. - On the statistical Lie groups of normal distributions
Jun-ichi Inoguchi
Information Geometry, 7, 2, 441, 447, Springer Science and Business Media LLC, 05 Oct. 2024, [Peer-reviewed], [International Magazine]
English, Scientific journal - Pseudo-symmetric almost Kenmotsu 3-manifolds
Jun-ichi Inoguchi; Ji-Eun Lee
Periodica Mathematica Hungarica, 89, 2, 388, 412, Springer Science and Business Media LLC, 08 Jul. 2024, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
Scientific journal - Parallel and totally umbilical hypersurfaces of the four‐dimensional Thurston geometry $\text{Sol}^4_0$
Marie D'haene; Jun‐ichi Inoguchi; Joeri Van der Veken
Mathematische Nachrichten, 297, 5, 1879, 1891, Wiley, 11 May 2024, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
Scientific journal, Abstract
We study hypersurfaces of the four‐dimensional Thurston geometry , which is a Riemannian homogeneous space and a solvable Lie group. In particular, we give a full classification of hypersurfaces whose second fundamental form is a Codazzi tensor—including totally geodesic hypersurfaces and hypersurfaces with parallel second fundamental form—and of totally umbilical hypersurfaces of . We also give a closed expression for the Riemann curvature tensor of , using two integrable complex structures. - Homogeneous geodesics of 4-dimensional solvable Lie groups
Jun-ichi Inoguchı
International Electronic Journal of Geometry, 17, 1, 106, 136, International Electronic Journal of Geometry, Person (Kazim ILARSLAN), 23 Apr. 2024, [Peer-reviewed], [Invited], [International Magazine]
Scientific journal,We study homogeneous geodesics in $4$-dimensional solvable Lie groups $\mathrm{Sol}_0^4$, $\mathrm{Sol}_1^4$, $\mathrm{Sol}_{m,n}$ and $\mathrm{Nil}_4$.
- Geodesics and magnetic curves in the 4-dim almost Kähler model space F4
Zlatko Erjavec; Jun-ichi Inoguchi
Complex Manifolds, 11, 1, Walter de Gruyter GmbH, 18 Apr. 2024, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
Scientific journal, Abstract
We study geodesics and magnetic trajectories in the model space F4{ { \rm{F } } }^{4}. The space F4{ { \rm{F } } }^{4} is isometric to the 4-dim simply connected Riemannian 3-symmetric space due to Kowalski. We describe the solvable Lie group model of F4{ { \rm{F } } }^{4} and investigate its curvature properties. We introduce the symplectic pair of two Kähler forms on F4{ { \rm{F } } }^{4}. Those symplectic forms induce invariant Kähler structure and invariant strictly almost Kähler structure on F4{ { \rm{F } } }^{4}. We explore some typical submanifolds of F4{ { \rm{F } } }^{4}. Next, we explore the general properties of magnetic trajectories in an almost Kähler 4-manifold and characterize Kähler magnetic curves with respect to the symplectic pair of Kähler forms. Finally, we study homogeneous geodesics and homogeneous magnetic curves in F4{ { \rm{F } } }^{4}. - Homogeneity of magnetic trajectories in the real special linear group
Jun-ichi Inoguchi; Marian Ioan Munteanu
Proceedings of the American Mathematical Society, 152, 3, 1287, 1300, American Mathematical Society (AMS), 18 Dec. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal, We prove the homogeneity of contact magnetic curves in the real special linear group of degree . Every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow. - On the $\eta$-parallelism in almost Kenmotsu $3$-manifolds
Jun-ichi Inoguchi; Ji-Eun Lee
Journal of the Korean Mathematical Society, 60, 6, 1303, 1336, Nov. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English - J-trajectories in 4-dimensional solvable Lie Group $\mathrm{Sol}_1^4$
Zlatko Erjavec; Jun-ichi Inoguchi
Journal of Nonlinear Science, 33, 6, Springer Science and Business Media LLC, 25 Sep. 2023, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Characteristic Jacobi operator on almost Kenmotsu $3$-manifolds
Jun-ichi Inoguchi
International Electronic Journal of Geometry, 16, 2, 464, 525, International Electronic Journal of Geometry, Person (Kazim ILARSLAN), 22 Sep. 2023, [Peer-reviewed]
English, Scientific journal,The Ricci tensor field, $\varphi$-Ricci tensor field and the characteristic Jacobi operator on almost Kenmotsu $3$-manifolds are investigated. We give a classification of locally symmetric almost Kenmotsu $3$-manifolds.
- Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles
Jun-ichi Inoguchi; Yoshiki Jikumaru; Kenji Kajiwara; Kenjiro T. Miura; Wolfgang K. Schief
Computer Aided Geometric Design, 105, 102233, 102233, Elsevier BV, Sep. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Minimal submanifolds in $\textrm{Sol}_1^4$
Zlatko Erjavec; Jun-ichi Inoguchi
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 117, 4, Springer Science and Business Media LLC, 22 Aug. 2023, [Peer-reviewed], ［Internationally co-authored］
Scientific journal - Contact 3-manifolds with pseudo-parallel characteristic Jacobi operator
Jun-ichi Inoguchi; Ji-Eun Lee
Mediterranean Journal of Mathematics, 20, 5, Springer Science and Business Media LLC, 05 Aug. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
Scientific journal - Minimal submanifolds in $\mathrm{Sol}_0^4$
Zlatko Erjavec; Jun-ichi Inoguchi
The Journal of Geometric Analysis, 33, 9, Springer Science and Business Media LLC, 16 Jun. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
Scientific journal - Killing Magnetic Curves in $\: \mathbb{H}^{3}$
Zlatko Erjavec; Jun-ichi Inoguchi
International Electronic Journal of Geometry, 16, 1, 181, 195, International Electronic Journal of Geometry, Person (Kazim ILARSLAN), 30 Apr. 2023, [Peer-reviewed]
Scientific journal,We consider magnetic curves corresponding to the Killing magnetic fields in hyperbolic 3-space.
- Pseudo-symmetric almost cosymplectic 3-manifolds
Jun-ichi Inoguchi; Ji-Eun Lee
International Journal of Geometric Methods in Modern Physics, World Scientific Pub Co Pte Ltd, 07 Apr. 2023, [Peer-reviewed], [Lead author]
English, Scientific journal - Killing submersions and magnetic curves
Jun-ichi Inoguchi; Marian Ioan Munteanu
Journal of Mathematical Analysis and Applications, 520, 2, 126889, 126889, Elsevier BV, Apr. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Magnetic unit vector fields
Jun-ichi Inoguchi; Marian Ioan Munteanu
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 117, 2, Springer Science and Business Media LLC, 20 Feb. 2023, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Magnetic Jacobi fields in Sasakian space forms
Jun-ichi Inoguchi; Marian Ioan Munteanu
Mediterranean Journal of Mathematics, 20, 1, Springer Science and Business Media LLC, 11 Dec. 2022, [Peer-reviewed], [Lead author], [International Magazine]
English, Scientific journal - Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group
Josef F. Dorfmeister; Jun-ichi Inoguchi; Shimpei Kobayashi
Complex Manifolds, 9, 1, 285, 336, Walter de Gruyter GmbH, 15 Nov. 2022, [Peer-reviewed]
English, Scientific journal, Abstract
We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will present a general scheme for how to construct minimal surfaces in Nil3 with non-trivial geometry. Special emphasis will be put on equivariant minimal surfaces. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group Iso◦(Nil3) of Nil3. - On some curves in 3-dimensional hyperbolic geometry and solvgeometry
Inoguchi, Jun-ichi
Journal of Geometry, 113, SPRINGER BASEL AG, 28 Jun. 2022, [Peer-reviewed]
English, Scientific journal, We study curve geometry in para-Sasakian 3-manifolds, especially in the hyperbolic 3-space and the space Sol3 of solvgeometry. Para- metric expression for φ-trajectories in the hyperbolic 3-space is given. - Almost cosymplectic 3-manifolds with pseudo-parallel characteristic Jacobi operator
Inoguchi, Jun-ichi; Lee, ji-Eun
International Journal of Geometric Methods in Modern Physics, 19, 8, WORLD SCIENTIFIC PUBL CO PTE LTD, Jun. 2022, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
English, Scientific journal, In this paper, we classify almost cosymplectic 3-manifolds with pseudo-parallel char- acteristic Jacobi operator. The only simply connected and complete non-cosymplectic almost cosymplectic 3-manifold with pseudo parallel characteristic Jacobi operator is the Minkowski motion group. - Biharmonic curves in f-Kenmotsu 3-manifolds
Inoguchi, Jun-ichi; Lee, ji-Eun
Journal of Mathematical Analysis and Applications, 509, 1, May 2022, [Peer-reviewed]
English, Scientific journal, It is known that there exist no proper biharmonic helices in Kenmotsu 3-manifolds. In this paper we show the existence of proper biharmonic helices in certain f-Kenmotsu 3-manifolds. - J-trajectories in 4-dimensional solvable Lie group Sol_0^4
Erjavec, Zlatko; Inoguchi, Jun-ichi
Mathematical Physics, Analysis and Geometry, 25, Mar. 2022, [Peer-reviewed]
English, Scientific journal - Magnetic Jacobi fields in 3-dimensional Sasakian space forms
Inoguchi, Jun-ichi; Munteanu; Marian Ioan
The Journal of Geometric Analysis, 32, 3, SPRINGER, Mar. 2022, [Peer-reviewed]
English, Scientific journal, Representative examples of uniform magnetic fields are furnished by Miller magnetic fields. From this point of view, magnetic Jacobi fields on surfaces or Kahler manifolds were investigated by Adachi and Gouda. On the contrary, Sasakian manifolds have non-uniform magnetic fields. We obtain all magnetic Jacobi fields along contact magnetic curves in 3-dimensional Sasakian space forms. - Gridshell structures with discrete curvature lines :Modeling technique and evaluation of mechanical performance
Yokosuka, Yohei; Inoguchi, Jun-ichi; Ohsaki, Makoto; Honma, Toshio
Proceedings of IASS Annual Symposia, IASS 2020/21 Surrey Symposium: Conceptual design, 821, 833, International Association for Shell and Spatial Structures (IASS), Jun. 2021, [Peer-reviewed]
English, International conference proceedings - ���� -Curves: controlled local curvature extrema
Miura; Kenjiro T; Gobithaasan, R. U; Salvi, Péter; Wang, Dan; Sekine, Tadatoshi; Usuki, Shin; Inoguchi, Jun-ichi; Kajiwara, Kenji
The Visual Computer, 38, 8, 2723, 2738, Springer, May 2021, [Peer-reviewed], ［Internationally co-authored］
English, Scientific journal, The kappa-curve is a recently published interpolating spline which consists of quadratic Bezier segments passing through input points at the loci of local curvature extrema. We extend this representation to control the magnitudes of local maximum curvature in a new scheme called extended- or is an element of kappa-curves. kappa-curves have been implemented as the curvature tool in Adobe Illustrator (R) and Photoshop (R) and are highly valued by professional designers. However, because of the limited degrees of freedom of quadratic Bezier curves, it provides no control over the curvature distribution. We propose new methods that enable the modification of local curvature at the interpolation points by degree elevation of the Bernstein basis as well as application of generalized trigonometric basis functions. By using is an element of kappa-curves, designers acquire much more ability to produce a variety of expressions, as illustrated by our examples. - Attractive curves. Expanding integrable geometry and discrete differential geometry
Inoguchi, Jun-ichi
SUGAKU, 73, 1, 88, 103, The Mathematical Society of Japan, Jan. 2021, [Peer-reviewed]
Japanese, Research society - A characterization of the alpha-connections on the statistical manifold of normal distributions
Furuhata, Hitoshi; Inoguchi, Jun-ichi; Kobayashi, Shimpei
Information Geometry, 4, 177, 188, SPRINGER, Oct. 2020, [Peer-reviewed]
English, Scientific journal - The Gauss maps of Demoulin surfaces with conformal coordinates
Inoguchi, Jun-ichi; Kobayashi, Shimpei
Science China Mathematics, 64, 7, 1479, 1492, SPRINGER, Oct. 2020, [Peer-reviewed]
English, Scientific journal, Demoulin surfaces in the real projective 3-space are investigated. Our result enables us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian 6-symmetric space. - Magnetic curves in the real special linear group
Inoguchi, Jun-ichi; Munteanu; Marian Ioan
Advances in Theoretical and Mathematical Physics, 23, 8, 2161, 2205, International Press, May 2020, [Peer-reviewed]
English, Scientific journal, We investigate contact magnetic curves in the real special linear group of degree 2. They are geodesics of the Hopf tubes over the projection curve. We prove that periodic contact magnetic curves in SL2R can be quantized in the set of rational numbers. Finally, we study contact homogeneous magnetic trajectories in SL2R and show that they project to horocycles in H-2(-4). - Generation of Discrete Log-aesthetic Curves based on Similarity Geometry and Euclidean Geometry
Miura,Kenjiro T; Kajiwara,Kenji; Inoguchi,Jun-ichi
Proceedings of JSPE Semestrial Meeting, 2019, 872, 873, The Japan Society for Precision Engineering, Sep. 2019
Japanese, Scientific journal, 近年の研究により，対数型美的曲線(log-aesthetic curve)は相似幾何により適切に定式化・解析できることが明らかとなった．本研究では，その離散化である離散対数型美的曲線（discrete log-aesthetic curve: dLAC）を相似幾何およびユークリッド幾何に基づいて生成する手法を提案する． - Discrete local induction equation
Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
Journal of Integrable Systems, 4, 1, Oxford University Press, Jun. 2019, [Peer-reviewed]
English, Scientific journal - Grassmann geometry on the 3-dimensional non-unimodular Lie groups
Inoguchi, Jun-ichi; Naitoh, Hiroo
Hokkaido Mathematical Journal, 48, 2, 385, 406, HOKKAIDO UNIV, DEPT MATHEMATICS, Jun. 2019, [Peer-reviewed]
English, Scientific journal, We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional non-unimodular Lie group with left invariant metric. This work together with our previous papers yield a complete classification of Grassmann geometry of orbit type in all 3-dimensional homogeneous spaces. - Magnetic curves in quasi-Sasakian 3-manifolds
Inoguchi, Jun-ichi; Munteanu; Marian Ioan; Nistor; Ana Irina
Analysis and Mathematical Physics, 9, 1, 43, 61, Springer, Mar. 2019, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
English, Scientific journal, We study magnetic trajectories corresponding to contact magnetic fields in 3-dimensional quasi-Sasakian manifolds. We show that they are slant curves, that is their contact angles are constant. We prove that such magnetic curves are geodesics for a certain linear connection for which all four structure tensor fields are parallel. - Generalization of log-aesthetic curves via similarity geometry
Inoguchi, Jun-ichi; Ziatdinov, Rushan; Miura; Kenjiro T
Japan Journal of Industrial and Applied Mathematics, 36, 1, 239, 259, Springer Japan, Jan. 2019, [Peer-reviewed]
English, Scientific journal, The class of log-aesthetic curves includes the logarithmic spiral, clothoid, and involute of a circle. Although most of these curves are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them, thereby presenting many applications in industrial and graphic design. The use of the log-aesthetic curves in practical design, however, is still limited. Therefore, we should extend its formula to obtain curves that solve various practical design problems such as ����
G^n Hermite interpolation, deformation, smoothing, data-point fitting, and blending plural curves. In this paper, we present a systematic approach to representing log-aesthetic curves via similarity geometry. In turn, this research provides a unified framework for various studies on log-aesthetic curves, particularly of log-aesthetic curve formulation. - Affine spheres and finite gap solutions of Tzitzèica equation
Inoguchi, Jun-ichi; Seiichi, Udagawa
Journal of Physics Communications, 2, 11, IOP Publishing home, Nov. 2018, [Peer-reviewed]
English, Scientific journal, The purpose of the present paper is to give an explicit form of the finite gap solutions to the Tzitzeica equation (2D Toda equation of type A_2^2) in terms of Riemann theta function. We give explicit expressions of proper affiene spheres derived from finite gap solutions to the Tzitzeica equation. - Magnetic curves in tangent sphere bundles II
Inoguchi, Jun-ichi; Munteanu; Marian Ioan
Journal of Mathematical Analysis and Applications, 466, 2, 1570, 1581, Elsevier, Oct. 2018, [Peer-reviewed], [Lead author], ［Internationally co-authored］, [International Magazine]
English, Scientific journal, We study contact magnetic curves in the unit tangent sphere bundle over the Euclidean plane. In particular, we obtain all contact magnetic curves which are slant. - Log-Aesthetic Curves: Similarity Geometry, Integrable Discretization and Variational Principles
Jun-ichi Inoguchi; Kenji Kajiwara; Kenjiro T. Miura; Hyeongki Park; Wolfgang K. Schief
arXiv:1808.03104, Aug. 2018
English, In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which is used in CAGD. We consider these curves in the context of similarity geometry and characterize them in terms of a ``stationary'' integrable flow on plane curves which is governed by the Burgers equation. We propose a variational principle for these curves, leading to the stationary Burgers equation as the Euler-Lagrange equation. As an application of the formalism developed here, we propose a discretization of both the curves and the associated variational principle which preserves the underlying integrable structure. We finally present an algorithm for the generation of discrete log-aesthetic curves for given ${\rm G}^1$ data. The computation time to generate discrete log-aesthetic curves is much shorter than that for numerical discretizations of log-aesthetic curves due to the avoidance of fine numerical integration to calculate their shapes. Instead, only coarse summation is required. - The hidden symmetry of chiral fields and the Riemann-Hilbert problem, revisited
井ノ口, 順一
京都大学数理解析研究所講究録, 2071, 1, 16, 京都大学数理解析研究所, Apr. 2018
Japanese, Research institution, We generalize the Ueno-Nakamura theory and the Uhlenbeck-Segal theory for harmonic maps of Riemann surfaces into compact semi-simple Lie groups to those of (affine) harmonic maps into general Lie groups with torsion free bi-invariant connection in terms of loop groups - Fairness metric of plane curves defined with similarity geometry invariants
Kenjiro T. Miura; Sho Suzuki; R. U. Gobithaasan; Shin Usuki; Jun-ichi Inoguchi; Masayuki Sato; Kenji Kajiwara; Yasuhiro Shimizu
Computer-Aided Design and Applications, 15, 2, 256, 263, Taylor and Francis Inc., 04 Mar. 2018, [Peer-reviewed]
English, Scientific journal - Log-aesthetic curves as similarity geometric analogue of Euler's elasticae
Jun-ichi Inoguchi; Kenji Kajiwara; Kenjiro T. Miura; Masayuki Sato; Wolfgang K. Schief; Yasuhiro Shimizu
Computer Aided Geometric Design, 61, 1, 5, Elsevier B.V., 01 Mar. 2018, [Peer-reviewed]
English, Scientific journal - 対数型美的曲線の相似幾何学的定式化
井ノ口, 順一
2018年度精密工学会春季大会シンポジウム資料集, 54, 57, Mar. 2018, [Invited]
Japanese, Symposium - Elasticae in similarity geometry and their discretization.
井ノ口, 順一; 梶原健司; 三浦憲二郎; 朴炯基; Schief, Wolfgang
Reports of RIAM Symposium No.29AO-S7 New Trends in Nonlinear Waves - Theory and Applications -, 29AO-S7, 61, 68, Research Institute for Applied Mechanics, Kyushu University, Mar. 2018, [Peer-reviewed]
Japanese, Symposium, 弾性エネルギーの臨界点である平面曲線は弾性曲線とよばれる．弾性曲線はmKdV 方程式と深く関連し，実際，平面曲線の等周変形を記述するmKdV 方程式の進行波解から定まる曲線が弾性曲線である．本稿では相似幾何学の枠組みを用いて工業意匠設計で用いられている対数型美的曲線（LAC）とその一般化を考察し，それらが平面曲線の等角変形を記述するBurgers 方程式の定常解として特徴付けられること，および適当なエネルギーの臨界点として定式化できることを報告する．この結果は，LAC が弾性曲線の相似幾何類似であることを示唆する．以上の理論的枠組みに基づき，可積分離散化の手法を応用したLAC の離散化を提案する．さらに，それらを離散変分問題の解として定式化する． - Periodic magnetic curves in Berger spheres
Jun-Ichi Inoguchi; Marian Ioan Munteanu
Tohoku Mathematical Journal, 69, 1, 113, 128, Tohoku University, Mathematical Institute, 01 Mar. 2017, [Peer-reviewed]
English, Scientific journal - Finite gap solutions for horizontal minimal surfaces of finite type in 5-sphere
Inoguchi, Jun-ichi; Taniguchi, Tetsuya; Seiichi, Udagawa
Journal of Integrable Systems, 1, 1, Oxford University Press, Dec. 2016, [Peer-reviewed]
English, Scientific journal - A loop group method for affine harmonic maps into Lie groups
Josef F. Dorfraeister; Jun-ichi Inoguchi; Shimpei Kobayashi
Advances in Mathematics, 298, 207, 253, Aug. 2016, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - Magnetic curves in cosymplectic manifolds
Simona-Luiza Druţă-Romaniuc; Jun-ichi Inoguchi; Marian Ioan Munteanu; Ana Irina Nistor
Reports on Mathematical Physics, 78, 1, 33, 48, Aug. 2016, [Peer-reviewed]
Scientific journal - dNLS Flow on Discrete Space Curves
Sampei Hirose; Jun-ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta
Mathematical Progress in Expressive Image Synthesis III, Mathematics for Industry, 24, 137, 149, Jun. 2016, [Peer-reviewed]
English, The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schr\"odinger equation (NLS). In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schr\"odinger equation (dNLS). We also present explicit formulas for both NLS and dNLS flows in terms of the $\tau$ function of the 2-component KP hierarchy. - On the Bernstein problem in the three-dimensional Heisenberg group
Josef F. Dorfmeister; Jun-ichi Inoguchi; Shimpei Kobayashi
Canadian Mathematical Bulletin, 59, 01, 50, 61, Mar. 2016, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
English, Scientific journal - A loop group method for minimal surfaces in the three-dimensional Heisenberg group
Josef F. Dorfmeister; Jun-Ichi Inoguchi; Shimpei Kobayashi
Asian Journal of Mathematics, 20, 3, 409, 448, 2016, [Peer-reviewed]
Scientific journal - dNLS Flow on Discrete Space Curves
Sampei Hirose; Jun-ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta
MI Lecture Note, 64, 93, 102, Sep. 2015, [Peer-reviewed]
English, International conference proceedings, The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schödinger equation (NLS). In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schrödinger equation (dNLS). We also present explicit formulas for both NLS and dNLS flows in terms of the tau function of the 2-component KP hierarchy. - Attractive plane curves in Differential Geometry
Inoguchi, Jun-ichi
MI Lecture Note, 64, 121, 124, Kyushu University, Sep. 2015, [Invited]
English, International conference proceedings - Harmonic maps in almost contact geometry
Inoguchi,Jun-ichi
SUT Journal of Mathematics, 50, 2, 353, 382, Dec. 2014, [Peer-reviewed]
English, Scientific journal, We study harmonicity and pluriharmonicity of holomorphic maps
in almost contact geometry. - Constant Gaussian curvature surfaces in the 3-sphere via loop groups
David Brander; Jun-ichi Inoguchi; Shimpei Kobayashi
Pacific Journal of Mathematics, 269, 2, 281, 303, 26 Jul. 2014, [Peer-reviewed]
Scientific journal - Discrete mKdV and discrete sine-Gordon flows on discrete space curves
Jun-ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 47, 23, 235202, Jun. 2014, [Peer-reviewed]
English, Scientific journal - Constant mean curvature surfaces in hyperbolic 3-space via loop groups
Josef F. Dorfmeister; Jun-ichi Inoguchi; Shimpei Kobayashi
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 686, 1, 36, Jan. 2014, [Peer-reviewed]
English, Scientific journal - Magnetic maps
Jun-Ichi Inoguchi; Marian Ioan Munteanu
International Journal of Geometric Methods in Modern Physics, 11, 6, 1450058, World Scientific Publishing Co. Pte Ltd, 2014, [Peer-reviewed]
English, Scientific journal - Gauss maps of constant mean curvature surfaces in three-dimensional homogeneous spaces
Jun-ichi Inoguchi; Joeri Van der Veken
Kobe Journal of Mathematics, 31, 1-2, 45, 62, 2014, [Peer-reviewed]
English, Scientific journal - Contact metric hypersurfaces in complex space forms
Jong Taek CHO; Jun-ichi INOGUCHI
Differential Geometry of Submanifolds and its Related Topics, 29 Oct. 2013, [Peer-reviewed], [Invited]
International conference proceedings - Integrable discretizations of the Dym equation
Bao-Feng Feng; Jun-ichi Inoguchi; Kenji Kajiwara; Ken-ichi Maruno; Yasuhiro Ohta
FRONTIERS OF MATHEMATICS IN CHINA, 8, 5, 1017, 1029, Oct. 2013, [Peer-reviewed]
English, Scientific journal - Semi-discrete analogues of the elastic beam equation and the short pulse equation
K. Maruno; B.F. Feng; J. Inoguchi; K. Kajiwara; Y. Ohta
Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications, 278, 281, Sep. 2013, [Peer-reviewed]
English, International conference proceedings, Two integrable nonlinear differential- difference systems, semi-discrete analogues of the Wadati-Konno-Ichikawa elastic beam equation and the short pulse equation, are constructed by using a geometric approach. - Biminimal curves in $2$-dimensional space forms
Jun-Ichi Inoguchi; Ji-Eun Lee
Communications of the Korean Mathematical Society, 27, 4, 771, 780, The Korean Mathematical Society, 31 Oct. 2012, [Peer-reviewed]
Scientific journal - MOTION AND BACKLUND TRANSFORMATIONS OF DISCRETE PLANE CURVES
Jun-ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta
KYUSHU JOURNAL OF MATHEMATICS, 66, 2, 303, 324, Sep. 2012, [Peer-reviewed]
English, Scientific journal - Affine biharmonic curves in 3-dimensional homogeneous geometries
Jun-ichi Inoguchi; Ji-Eun Lee
Mediterranean Journal of Mathematics, 10, 1, 571, 592, 20 Apr. 2012, [Peer-reviewed]
Scientific journal - Minimal translation surfaces in the Heisenberg group $\mathrm{Nil}_3$
Jun-ichi Inoguchi; Rafael López; Marian-Ioan Munteanu
Geometriae Dedicata, 161, 1, 221, 231, 25 Feb. 2012, [Peer-reviewed]
Scientific journal - Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves
Jun-ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45, 4, 045206, Feb. 2012, [Peer-reviewed]
English, Scientific journal - Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves
Bao-Feng Feng; Jun-ichi Inoguchi; Kenji Kajiwara; Ken-ichi Maruno; Yasuhiro Ohta
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44, 39, 395201, Sep. 2011, [Peer-reviewed]
English, Scientific journal - semi-discrete modified KdV方程式と平面離散曲線の時間発展
井ノ口順一; 梶原健司; 松浦望; 太田泰広
九州大学応用力学研究所研究集会報告, 22AO-S8, 75, 81, Mar. 2011, [Peer-reviewed]
Japanese, Research institution - Grassmann geometry on the 3-dimensional unimodular lie groups II
Jun-Ichi Inoguchi; Hiroo Naitoh
Hokkaido Mathematical Journal, 40, 3, 411, 429, 2011, [Peer-reviewed]
English, Scientific journal - On $\varphi$-Einstein contact Riemannian manifolds
Jong Taek Cho; Jun-ichi Inoguchi
Mediterranean Journal of Mathematics, 7, 2, 143, 167, 22 Apr. 2010, [Peer-reviewed]
Scientific journal - Grassmann geometry on the 3-dimensional unimodular Lie groups I
Jun-ichi Inoguchi; Hiroo Naitoh
HOKKAIDO MATHEMATICAL JOURNAL, 38, 3, 427, 496, Aug. 2009, [Peer-reviewed]
English, Scientific journal - LIGHTLIKE SURFACES IN MINKOWSKI 3-SPACE
Jun-Ichi Inoguchi; Sungwook Lee
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 6, 2, 267, 283, Mar. 2009, [Peer-reviewed]
English, Scientific journal - A complete classification of parallel surfaces in three-dimensional homogeneous spaces
Jun-ichi Inoguchi; Joeri Van der Veken
GEOMETRIAE DEDICATA, 131, 1, 159, 172, Feb. 2008, [Peer-reviewed]
English, Scientific journal - A Weierstrass type representation for minimal surfaces in Sol
Jun-Ichi Inoguchi; Sungwook Lee
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136, 6, 2209, 2216, 2008, [Peer-reviewed]
English, Scientific journal - Parallel surfaces in the motion groups E(1,1) and E(2)
Inoguchi, Jun-ichi; Van der Veken, Joeri
Bulletin of the Belgian Mathematical Society - Simon Stevin, 14, 2, 321, 332, Belgian Mathematical Society, Jun. 2007, [Peer-reviewed]
English, Scientific journal, We give a classification of parallel surfaces in the groups of rigid motions of Minkowski plane and Euclidean plane, equipped with a general left-invariant metric. Our result completes the classification of parallel surfaces in the eight three-dimensional model geometries of Thurston and in three-dimensional unimodular Lie groups with maximal isometry group. - Pseudo-symmetric contact 3-manifolds II - When is the tangent sphere bundle over a surface pseudo-symmetric?
Jong Taek Cho; Jun-ichi Inoguchi
Note di Matematica, 27, 1, 119, 129, 2007, [Peer-reviewed]
English, Scientific journal - Biminimal submanifolds in contact 3-manifolds
Jun-ichi Inoguchi
BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 12, 1, 56, 67, 2007, [Peer-reviewed]
English, Scientific journal - On slant curves in Sasakian 3-manifolds
Jong Taek Cho; Jun-ichi Inoguchi; Ji-Eun Lee
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 74, 3, 359, 367, Dec. 2006, [Peer-reviewed]
English, Scientific journal - Characterizations of Bianchi-Backlund transformations of constant mean curvature surfaces
S Kobayashi; J Inoguchi
INTERNATIONAL JOURNAL OF MATHEMATICS, 16, 2, 101, 110, Feb. 2005, [Peer-reviewed]
English, Scientific journal - Timelike minimal surfaces via loop groups
J. Inoguchi; M. Toda
Acta Applicandae Mathematicae, 83, 3, 313, 355, Sep. 2004, [Peer-reviewed], [Lead author]
Scientific journal - Schrodinger flows, binormal motion for curves and the second AKNS-hierarchies
Q Ding; J Inoguchi
CHAOS SOLITONS & FRACTALS, 21, 3, 669, 677, Jul. 2004, [Peer-reviewed]
English, Scientific journal - Invariant minimal surfaces in the real special linear group of degree 2
Jun-ichi Inoguchi
Italian Journal of Pure and Applied Mathematics, 16, 61, 80, 2004, [Peer-reviewed]
English, Scientific journal - Minimal surfaces in 3-dimensional solvable Lie groups
J Inoguchi
CHINESE ANNALS OF MATHEMATICS SERIES B, 24, 1, 73, 84, Jan. 2003, [Peer-reviewed]
English, Scientific journal - Timelike Bonnet surfaces in Lorentzian space forms
A Fujioka; J Inoguchi
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 18, 1, 103, 111, Jan. 2003, [Peer-reviewed]
English, Scientific journal - On time-like surfaces of positive constant Gaussian curvature and imaginary principal curvatures
C.H. Gu; H.S. Hu; Jun-Ichi Inoguchi
Journal of Geometry and Physics, 41, 4, 296, 311, Elsevier BV, Apr. 2002, [Peer-reviewed], ［Internationally co-authored］
English, Scientific journal - Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces
Mohamed Belkhelfa; Franki Dillen; Jun-ichi Inoguchi
PDEs, Submanifolds and Affine Differential Geometry, 67, 87, Institute of Mathematics Polish Academy of Sciences, 2002, [Peer-reviewed]
English, International conference proceedings - Darboux transformations on timelike constant mean curvature surfaces
J Inoguchi
JOURNAL OF GEOMETRY AND PHYSICS, 32, 1, 57, 78, Nov. 1999, [Peer-reviewed]
English, Scientific journal - On some generalisations of constant mean curvature surfaces
Atsushi Fujioka; Jun-ichi Inoguchi
Lobachevskii Journal of Mathematics, 3, 73, 95, 1999, [Peer-reviewed]
English, Scientific journal - Timelike surfaces of constant mean curvature in Minkowski 3-space
Jun-ichi INOGUCHI
Tokyo Journal of Mathematics, 21, 1, Tokyo Journal of Mathematics, 01 Jun. 1998, [Peer-reviewed]
Scientific journal - Bonnet surfaces with constant curvature
Atsushi Fujioka; Jun-ichi Inoguchi
Results in Mathematics, 33, 3-4, 288, 293, Springer Science and Business Media LLC, May 1998, [Peer-reviewed]
Scientific journal
- 曲面と解析力学（特集 曲線と曲面を考える）
井ノ口順一, 数理科学, 62, 2, 54, 61, Feb. 2024
Japanese - Sine-Gordon方程式の解法とその離散化
宇田川 誠一; 井ノ口 順一; 梶原 健司, 日本大学医学部一般教育研究紀要 / 日本大学医学部一般教育 編, 50, 9, 26, Dec. 2022
日本大学医学部, Japanese - Affine connections and Contact Structure
Jun-ichi Inoguchi, Geometry and Analysis Fukuoka, 11, 34, Mar. 2022, [Invited]
Japanese - 相似概念の獲得と理解を促す授業展開の一例． 身のまわりの題材や中点連結定理を導く課題を通して
草桶勇人; 山本一海; 井ノロ順一; 伊禮三之, 福井大学教育実践研究, 39, 77, 87, 13 Feb. 2015, [Domestic magazines]
福井大学教育地域科学部附属教育実践総合センター - Deformation of Space Discrete Curves by Discrete mKdV and Discrete Sine-Gordon Equations (Novel Development of Nonlinear Discrete Integrable Systems)
INOGUCHI Jun-ichi; KAJIWARA Kenji; MATSUURA Nozomu; OHTA Yasuhiro, RIMS Kokyuroku Bessatsu, 47, 1, 21, Jun. 2014
"Novel Development of Nonlinear Discrete Integrable Systems". September 2～4, 2013. edited by Junta Matsukidaira. The papers presented in this volume of RIMS Kokyuroku Bessatsu are in final form and refereed., Kyoto University - Submanifold geometry of contact 3-manifolds (Development in Differential Geometry of Submanifolds)
Inoguchi Jun-ichi, RIMS Kokyuroku, 1880, 72, 99, Apr. 2014
Kyoto University - 自己適合移動格子スキームとミンコフスキー平面上の離散曲線の運動について
丸野健一; 梶原健司; 井ノ口順一; 太田泰広; FENG Baofeng, 日本応用数理学会年会講演予稿集(CD-ROM), 2014, 2014 - Discrete differential geometry of surfaces (Progress in Mathematics of Integrable Systems)
Inoguchi Jun-ichi, RIMS Kokyuroku Bessatsu, 30, 77, 99, Apr. 2012
Kyoto University - しゃぼん玉は本当に丸い？
井ノ口順一, SCITA NEWS, 11, 1, 1, Mar. 2011, [Invited]
Japanese, Others - 離散平面曲線の時間発展に現れる離散可積分系と離散ホドグラフ変換
FENG Baofeng; 井ノ口順一; 梶原健司; 丸野健一; 太田泰広, 日本応用数理学会年会講演予稿集, 2011, 2011 - A note on almost contact Riemannian 3-manifolds
Inoguchi Jun-ichi, Bulletin of the Yamagata University. Natural science, 17, 1, 1, 6, 15 Feb. 2010
We investigate curvatures of normal almost contact Riemannian 3-manifolds. In particular, we show that Kenmotsu 3-manifolds of constant scalar curvature are of constant curvature, Yamagata University, English - 手遊びの算数（２）
井ノ口順一, 子どもの遊びと手の労働, 17, 18, May 2009, [Invited] - 手遊びの算数（１）
井ノ口順一, 子どもの遊びと手の労働, 15, 16, May 2009, [Invited]
Japanese - On homogeneous contact 3-manifolds
Inoguchi Jun-ichi, Bulletin of the Faculty of Education, Utsunomiya University, 59, 1, 12, 10 Mar. 2009
Utsunomiya University, English - 戸田方程式と微分幾何
井ノ口順一, 戸田格子40周年 非線形波動研究の歩みと展望, 47, 62, 2008 - 多角形の角における発展的・統合的な見方・考え方の指導
石川佳広; 井ノ口順一; 木村寛, 宇都宮大学教育学部教育実践総合センター紀要, 30, 443, 452, 01 Jul. 2007, [Domestic magazines]
宇都宮大学教育学部教育実践総合センター, Japanese, Report research institution - Pseudo-symmetric Lie groups of dimension 3
Inoguchi, Jun-ichi, Bulletin of the Faculty of Education, Utsunomiya University. Section 2, 51, 1, 5, Mar. 2007 - 「ベンフォードの法則」の授業について
井ノ口順一; 黒崎貞雄, 宇都宮大学教育学部教育実践総合センター紀要, 29, 117, 121, 01 Jul. 2006, [Lead author]
宇都宮大学教育学部教育実践総合センター, Japanese, Report research institution - Geometry, it's a secret ingredient that makes integrable system theory interesing for us (Perspective and Application of Integrable Systems)
Inoguchi Jun-ichi, RIMS Kokyuroku, 1422, 134, 153, Apr. 2005
Kyoto University, Japanese - Integrable systems in unfashionable geometries (Theory of integrable systems and related topics : State of arts and perspectives)
Inoguchi Jun-ichi, RIMS Kokyuroku, 1400, 127, 144, Nov. 2004
Kyoto University - A QUICK INTRODUCTION TO DISCRETISED PROJECTIVE DIFFERENTIAL GEOMETRY (Development in Discrete Integrable Systems : Ultra-Discretization, Quantization)
Inoguchi Jun-ichi, RIMS Kokyuroku, 1221, 112, 124, Jul. 2001
Kyoto University, Japanese - INTEGRABLE SURFACES AND THEIR DISCRETISATION (Recent Topics on Discrete Integrable Systems)
Inoguchi Jun-Ichi, RIMS Kokyuroku, 1170, 9, 22, Sep. 2000
Kyoto University, Japanese - Bonnet Surfaces with Constant Curvature (Homogeneous Structures and Theory of Submanifolds)
Fujioka Atsushi; Inoguchi Jun-ichi, RIMS Kokyuroku, 1069, 73, 82, Nov. 1998
Kyoto University, Japanese - SURFACES IN MINKOWSI 3-SPACE AND HARMONIC MAPS
INOGUCHI JUN-ICHI, RIMS Kokyuroku, 995, 58, 69, May 1997
Kyoto University, English
- リッカチのひ・み・つ［増補版］
井ノ口 順一
日本評論社, 14 Jan. 2026, 9784535790360 - Multilinear Algebra I. Tensors and Exterior Algebras
Inoguchi Jun-ichi
現代数学社, 21 Feb. 2025, 9784768706558, 360, Japanese, [Single work] - Textbook: Analytic Geometry and Linear Algebra
Inoguchi Jun-ichi
現代数学社, 21 May 2024, 9784768706350, 360, Japanese, [Single work] - 1+3 dimensional world: From Surfcaes to Manifolds and Spacetimes
Inoguchi, Jun-ichi
Gendai Sugakusha, 21 Apr. 2023, 9784768706046, 268, Japanese, Scholarly book, [Single work] - Contact Geometry of Slant Submanifolds
Inoguchi, Jun-ichi; Munteanu; Marian Ioan, Slant Curves and Magnetic Curves
Springer Nature Singapore Pte Ltd., Jun. 2022, 9789811600166, English, Scholarly book, This chapter treats slant curves and magnetic curves in almost contact metric manifolds. Special attention is paid to magnetic curves in Sasakian manifolds. We describe magnetic slant curves in Sasakian space forms., [Contributor] - 1+2 dimensional world: Curves and Surfaces in Minkowski Space
Inoguchi, Jun-ichi
Gendai Sugakusha, 21 Feb. 2022, 9784768705766, 204, Japanese, Scholarly book, [Single work] - 1+1 dimensional world: Geometry of Minkowski Plane
Inoguchi, Jun-ichi
現代数学社, 21 Dec. 2021, 189, Japanese, Scholarly book, [Single work] - A First Course to Vector Analysis
Inoguchi, Jun-ichi
現代数学社, 21 Dec. 2020, 9784768705476, 396, Japanese, Scholarly book, [Single work] - A First Course to Partial differentiation
Inoguchi, Jun-ichi
現代数学社, 01 Sep. 2019, 9784768705162, 222, Japanese, Scholarly book, [Single work] - 解析学百科II 可積分系の数理
Inoguchi, Jun-ichi, 幾何学と可積分系
朝倉書店, 20 Mar. 2018, 9784254117271, Japanese, Scholarly book, [Contributor] - A First Course to Lie Algebras
Inoguchi, Jun-ichi
現代数学社, 23 Feb. 2018, 9784768704714, 280, Japanese, Scholarly book, [Single work] - A First Course to Lie Groups
Inoguchi, Jun-ichi
現代数学社, Jul. 2017, 9784768704707, 272, Japanese, Scholarly book, [Single work] - Surface Geometry and Integrable Systems
Inoguchi,Jun-ichi
Asakura Publishing Co., Ltd., 25 Oct. 2015, 9784254117684, vi, 212p, Japanese, Scholarly book, [Single work] - 応用数理ハンドブック
Inoguchi, Jun-ichi, 幾何学と可積分系
Asakura Publishing Co., Ltd., 15 Nov. 2013, 9784254111415, Japanese, Scholarly book, [Contributor] - 負定曲率曲面とサイン・ゴルドン方程式
Inoguchi, Jun-ichi
Saitama University, Apr. 2012, Japanese, Scholarly book, [Single work] - 離散可積分系・離散微分幾何チュートリアル2012
Inoguchi, Jun-ichi, 可積分幾何入門
Kyushu University, Mar. 2012, Japanese, Scholarly book, [Contributor] - リッカチのひ・み・つ
Inoguchi, Jun-ichi
日本評論社, Sep. 2010, Japanese, Scholarly book, [Single work] - どこにでも居る幾何. アサガオから宇宙まで
Inoguchi, Jun-ichi
日本評論社, Sep. 2010, 9784535786110, Japanese, Scholarly book, [Single work] - Plane curves and Solitons
Inoguchi, Jun-ichi
Asakura Publishing Co., Ltd., 10 Mar. 2010, 9784254117349, Japanese, Scholarly book, [Single work] - いろいろな幾何と曲線の時間発展 (Hokkaido University technical report series in mathematics 138)
Inoguchi, Jun-ichi
Hokkaido University, 10 Sep. 2008, Japanese, Scholarly book, [Single work] - 幾何学いろいろ
Inoguchi, Jun-ichi
日本評論社, Nov. 2007, 9784535784628, Japanese, Scholarly book, [Single work] - 曲面の微分幾何学とソリトン方程式 : 可積分幾何入門
Inoguchi, Jun-ichi, 負定曲率曲面とサイン・ゴルドン方程式
立教大学, Oct. 2005, Japanese, Scholarly book, [Contributor]
- 対称R空間としての球面と射影空間
井ノ口 順一
東京理科大学幾何学セミナー, 16 Mar. 2026, Japanese, Public discourse
[Invited] - 大きな群の幾何学 1
井ノ口順一
宇都宮微分幾何学研究集会2025, 13 Dec. 2025, English, Invited oral presentation
13 Dec. 2025 - 14 Dec. 2025, [Invited], [Domestic Conference] - 大きな群の幾何学 2
井ノ口順一
宇都宮微分幾何学研究集会2025, 14 Dec. 2025, English, Invited oral presentation
[Invited] - 数学における「主体的、対話的で深い学び」とは？
井ノ口順一
椙山女学園大学セミナー, 11 Dec. 2025, Japanese, Public discourse
[Invited] - 産業を支える微分幾何学
井ノ口順一
椙山女学園大学セミナー, 11 Dec. 2025, Japanese, Public discourse
[Invited] - ３次元空間内の曲面と可積分系
井ノ口順一
大阪大学大学院理学研究科数学専攻談話会, 01 Dec. 2025, English, Others
Japan, [Invited] - 可積分系入門（１）
井ノ口 順一
波動セミナー（北海道大学）, 26 Nov. 2025, Japanese, Public discourse - Surface geometry of Nil
Jun-ichi Inoguchi
YNU Geometry and Topology Seminar, 24 Oct. 2025, Japanese, Public discourse
Japan, [Invited] - Projective minimal surfaces and harmonic maps
Jun-ichi Inoguchi
Workshop on the Geometry of Submanifolds, 17 Aug. 2025, The Geometry Research Group at Beihang University, English, Invited oral presentation
Beijing, China, [Invited] - Surfaces in 3-dimensional spaces and Integrable systems
Jun-ichi Inoguchi
Tuesday Seminar on Topology ( Home Contact Text only print | Full screen print Liaison Office Library Publications Academic archive MSUT Video archive Tambara Institute Visitor information Forefront Physics and Mathematics Program to Drive Transformation World-leading Innovative Graduate Study for Frontiers of Mathematical Sciences and Physics The University of Tokyo Foundation Contact Graduate School of Mathematical Sciences, The University of Tokyo), 03 Dec. 2024, Japanese, Invited oral presentation
[Invited] - Homogeneous geometry of statistical manifolds (1), (2)
井ノ口順一
ミニワークショップ 統計多様体の幾何学とその周辺 (16), 30 Nov. 2024, Japanese, Invited oral presentation
Japan, [Invited], [Domestic Conference] - 線織面の話題から
井ノ口 順一
第25回水戸幾何セミナー, 21 Nov. 2024, Japanese, Invited oral presentation
[Invited] - Homogeneous Riemannian structures of the model spaces of Thurston geometry
Jun-ichi Inoguchi
東京理科大学 創域理工学部数理科学科 談話会, 01 Nov. 2024, Japanese, Public discourse
[Invited] - Grassmann geometry on $H^2\times R$
Jun-ichi Inoguchi
TUS Geometry Seminar, 01 Nov. 2024, Japanese, Public discourse
[Invited] - Surface geometry in $H^2\times R$
Jun-ichi Inoguchi
YNU Geometry and Topology Seminar, 25 Oct. 2024, Japanese, Public discourse
[Invited] - Geometric modeling for robotic surfaces based on Wente torus
岩本憲泰; 井ノ口順一
The Robotics and Mechatronics Conference 2024 in Utsunomiya (ROBOMECH2024 in Utsunomiya), 31 May 2024, Robotics and Mechatronics Division, The Japan Society of Mechanical Engineers, Japanese, Oral presentation
Utsunomiya, Japan, Robotic surfaces composed of soft materials significantly differ in their actuation elements and structures, making the development of universally applicable theories for robotic surfaces challenging. To consider common elements independent of the specific actuation elements or structures of these robots, a geometric surface model is necessary. The authors have previously proposed the use of surfaces of constant mean curvature, specifically revolution surfaces, in the kinematics of robotic surfaces. This paper proposes modeling using a part of the Wente torus. By varying a region on the Wente torus and its scale, we demonstrate the capability to represent a diverse array of shapes without a rotation axis, unlike traditional models., [Domestic Conference] - 3次元接触多様体の磁場軌道
井ノ口順一
接触構造、特異点、微分方程式及びその周辺, 19 Jan. 2024, Japanese, Oral presentation
金沢大学サテライト・プラザ, Japan - Differential Geometry of Industrial Shape Design
Jun-ichi Inoguchi
第22回水戸幾何セミナー, 17 Nov. 2023, Japanese, Invited oral presentation
[Invited], [Domestic Conference] - Contact geometry and magnetic trajectories
Jun-ichi Inoguchi
YNU Geometry and Topology Seminar, 27 Oct. 2023, Japanese, Public discourse
[Invited] - Discrete Differential Geometry. Developments and Perspectives
Jun-ichi Inoguchi
日本建築学会大会（近畿）構造部門（シェル・空間構造）パネルディスカッション, 12 Sep. 2023, Japanese, Nominated symposium
[Invited] - Submanifold Geometry of LCK surfaces
Jun-ichi Inoguchi
The 20th Mito Geometry Seminar, 24 Feb. 2023, Japanese, Invited oral presentation
[Invited] - Lie sphere geometry: Is it future promising?
Jun-ichi Inoguchi
Mini-Workshop "Differential Geometry, Integrable Systems, and Shape Generation", 16 Feb. 2023, Japanese, Invited oral presentation
[Invited] - アフィン接続と接触構造に関する話題から
井ノ口, 順一
福岡大学 微分幾何研究会, 05 Nov. 2021, Japanese, Oral presentation
福岡大学（ハイブリッド）, [Invited], [Domestic Conference] - Similarity geometry revisited: Differential geometry and CAGD
井ノ口, 順一
8th European Congress of Mathematics (8ECM) Minisymposium Differential Geometry: Old and New, 22 Jun. 2021, European Mathematical Society, English, Oral presentation
スロベニア Portoroz, [Invited], [International presentation] - リー球面幾何による離散曲率線グリッドシェル構造の形状決定法
横須賀洋平; 井ノ口順一; 大崎純; 本間俊雄
日本応用数理学会第17回 研究部会連合発表会, 05 Mar. 2021, Japanese, Oral presentation
法政大学小金井キャンパス（オンライン）, Japan, 本稿では、リー球面幾何に基づく離散曲面を用いた離散曲率線によるグリッドシェル構造を提案する。離散曲面の主曲率方向を細分化することで、誤差がなく区分的に滑らかな離散曲率線を構成したグリッドシェル構造を構築する。離散曲率線によるグリッドシェル構造は、一軸の曲げ加工のみで湾曲した曲線部材を製作することができる優れた施工性・製作性を有することを示す。, [Domestic Conference] - 「離散微分幾何と有限要素法の融合，建築とCGへの応用」
井ノ口, 順一
AIMaP集会「離散微分幾何と有限要素法の融合，建築とCGへの応用」, 23 Dec. 2020, 筑波大学数理科学研究コア, Japanese, Others
九州大学（ハイブリッド）, [Domestic Conference] - 3次元球面内の曲線に関する話題
井ノ口, 順一
北川義久教授ご退職記念研究集会, 13 Nov. 2020, Japanese, Oral presentation
東京工業大学（オンライン）, [Invited], [Domestic Conference] - Tzitzeica方程式をめぐって
井ノ口, 順一
リーマン面に関連する 位相幾何学, 17 Aug. 2020, Japanese, Oral presentation
東京大学（オンライン）, [Invited], [Domestic Conference] - Slant curves in contact geometry
井ノ口, 順一
International Workshop on Geometry of Submanifolds, 2019, 08 Nov. 2019, English, Oral presentation
トルコ Istanbul center for mathematical Science, [Invited], [International presentation] - 3次元等質空間内の曲面のグラスマン幾何
井ノ口, 順一
北九州幾何学研究集会2019, 06 Jul. 2019, Japanese, Oral presentation
九州工業大学, [Invited], [Domestic Conference] - Harmonic map into Lie groups, revisited
井ノ口, 順一
The Joint International Meeting of the Chinese mathematical Society and American Mathematical Society, 11 Jun. 2018, English, Oral presentation
中華人民共和国 復旦大学, [Invited], [International presentation] - Curve flows, integrable systems and industrial design
井ノ口, 順一
Integrable Geometry at Bayrischzell, 18 May 2018, English, Oral presentation
ドイツ Bayrischzell Gasthof zur Post, [Invited], [International presentation] - 対数型美的曲線の相似幾何学的定式化
井ノ口, 順一
AIMaP数学応用シンポジウム：精密工学と幾何学の新たな出会い, 17 Mar. 2018, 公益社団法人 精密工学会, Japanese, Oral presentation
中央大学, [Invited], [Domestic Conference] - Elasticae in similarity geometry and their discretization.
井ノ口, 順一; 梶原健司; 三浦憲二郎; 朴炯基; Schief, Wolfgang
非線形波動研究の新潮流 .理論とその応用, 11 Nov. 2017, Japanese, Oral presentation
九州大学応用力学研究所, [Domestic Conference] - Grassmann geometry of surfaces in 3-dimensional homogeneous spaces
井ノ口, 順一
INTERNATIONAL CONFERENCE ON APPLIED AND PURE MATHEMATICS (ICAPM 2017), 02 Nov. 2017, English, Keynote oral presentation
ルーマニア "Gheorghe Asachi" Technical University, Iaşi, [Invited], [International presentation] - 相似幾何不変量による平面曲線 の Fairness 測度
三浦憲二郎; 鈴木晶; 臼杵深; Gobithaasan, Rudrusamy; 井ノ口, 順一; 佐藤雅之; 梶原健司; 清水保弘
日本応用数理学会2017年度年会, 08 Sep. 2017, Japanese, Oral presentation
武蔵野大学, [Domestic Conference] - 対数型美的曲線の相似幾何における平面曲線に対する変分原理による 定式化
井ノ口, 順一; 梶原健司; 三浦憲二郎; Schief, Wolfgang
日本応用数理学会2017年度年会, 08 Sep. 2017, Japanese, Oral presentation
武蔵野大学, [Domestic Conference] - Planar Curves and Industrial Design
井ノ口順一
第63回幾何学シンポジウム（岡山大学）, 28 Aug. 2016, Japanese, Invited oral presentation
岡山大学, [Invited], [Domestic Conference] - Grasmann geometry of 3-dimensional homogeneous spaces
井ノ口順一
内藤博夫先生退職記念研究集会, 05 Mar. 2016, Japanese
山口大学, [Invited], [Domestic Conference] - 魅力的な曲線たち
井ノ口順一
日本数学会北海道支部会, 03 Dec. 2015, 日本数学会北海道支部会, Japanese, Invited oral presentation
北海道大学, [Invited], [Domestic Conference] - Attractive plane curves in Differential Geometry
Inoguchi,Jun-ichi
Mathematical Progress in Expressive Image Synthesis 2015, 25 Sep. 2015, 九州大学, English, Invited oral presentation
日本 九州大学, [Invited], [Domestic Conference] - New examples of biharmonic hypersurfaces
井ノ口順一
International Workshop on Finite Type Submanifolds, 2014, 03 Sep. 2014, English, Oral presentation
トルコ イスタンブール工科大学, [International presentation] - Minimal surfaces in the Heisenberg group
Inoguchi, Jun-ichi
Japanese-Spanish Workshop on Differential Geometry 2, 05 Feb. 2014, English
東京工業大学, [Invited], [Domestic Conference] - 曲線・曲面の可積分幾何
井ノ口 順一
大岡山談話会, 13 Jun. 2012
[Invited] - 差分幾何
井ノ口順一
第58回幾何学シンポジウム（山口大学）, 30 Aug. 2011
[Invited] - Constant mean curvature surfaces in hyperbolic 3-space
Inoguchi, Jun-ichi
Japanese-Spanish Workshop on Differential Geometry, 14 Feb. 2011, English, Keynote oral presentation
[Invited] - 3次元双曲空間の平均曲率一定曲面（特別講演）
井ノ口順一
日本数学会秋季総合分科会幾何学分科会（名古屋大学）, 23 Sep. 2010, Japanese, Invited oral presentation
[Invited] - 取り扱いの難しい可積分方程式（特別講演）
井ノ口順一
非線形波動研究の現状と課題. 次の10 年への展望（九州大学応用力学研究所）, 19 Nov. 2009, Invited oral presentation
[Invited] - 3次元双曲空間の平均曲率一定曲面
井ノ口順一
第56回幾何学シンポジウム（佐賀大学）, 30 Aug. 2009
[Invited] - Bianchi surfaces in space forms
Inoguchi, Jun-ichi
Advences in Surface Theory (Kloster Benediktbeuern, Germany), 24 Jan. 2005, English
[Invited] - 非線性達朗貝弥公式与古典弦模型（基調講演）
井ノ口順一
微分幾何与可積系統討論会（復旦大学数学研究所）, 06 Jan. 2003, English
[Invited] - On Kinnersley-Chitre theory on stationary axially symmetric Einstein equations
Inoguchi, Jun-ichi
Overseminar differentialgeometrie, Universitat Augsburg, 01 Mar. 2002, English
[Invited] - 非線型ダランベール公式についてI, II（総合講演）
井ノ口順一
第48回幾何学シンポジウム（茨城大学）, 29 Aug. 2001, Japanese, Keynote oral presentation
[Invited] - Integrable surfaces in Lorentzian Geometry"
Jun-ichi Inoguchi
MSJIRI 9 Integrable Systems in Differential Geometry, 19 Jul. 2000, English, Invited oral presentation
[Invited], [International presentation] - Minimal surfaces in 3-dimensional homogeneous spaces"
Jun-ichi Inoguchi
Workshop on Harmonic Maps and Curvature Properties of Submanifolds 2, 12 Apr. 2000, English, Invited oral presentation
[Invited] - Soliton theoretic approach to surface geometry（全体講演）
井ノ口順一
第46回幾何学シンポジウム（東京大学）, 04 Aug. 1999, Invited oral presentation - 平均曲率一定曲面の一般化．可積分性理論の観点から
藤岡敦; 井ノ口順一
第45回幾何学シンポジウム（筑波大学）, 06 Aug. 1998 - 曲面の微分幾何学とソリトン方程式
井ノ口順一
第44回幾何学シンポジウム（信州大学）, 20 Aug. 1997, Japanese, Invited oral presentation
[Invited]
- 代数学・幾何学序論, 2024年, 学士課程, 理学部
- 幾何学演習Ａ, 2024年, 学士課程, 理学部
- 幾何学Ａ, 2024年, 学士課程, 理学部
- 線形代数学Ⅰ, 2024年, 学士課程, 全学教育
- 幾何学演習, 2024年, 学士課程, 理学部
■ Research Themes
- Construction of constant mean curvature surfaces via loop groups and Lorentz geometry
Grants-in-Aid for Scientific Research
01 Apr. 2023 - 31 Mar. 2027
井ノ口 順一
本研究の主要課題である「ループ群とローレンツ幾何による等質空間内の平均曲率一定曲面の構成」に関し、等質空間の幾何学の観点から研究を遂行し以下の研究成果を得た。
（１）双曲平面H2と直線の直積であるH2xRはサーストン幾何学におけるモデル空間の一つでありローレンツ群SO(2,1)と直線の直積群SO(2,1)xRを等長変換群にもつ。また可解リー群の構造を備えている。以前の研究において８種の空間の軌道型曲面のグラスマン幾何の存在問題を解決した。過去の研究成果を再精査し、H2xRの軌道型曲面はH2xRの平均曲率一定曲面の基本的な例を与えることが確認された。この発見を出発点とし、可解リー群の構造とグラスマン幾何の理論を組み合わせることにより軌道型曲面を全て具体的に記述することに成功した（内藤氏との共著論文を準備中）。（２）H2xRのグラスマン幾何に関連し、前研究課題（19K03461）ではH2を等質部分多様体または複素部分多様体として含む４次元等質空間の部分多様体論を創始した。前研究課題において得られていたSol4_0およびSol4_1の極小部分多様体の（いくつかの条件下での）分類を改良し、研究成果を論文として発表した。（３）リーマン幾何学に類似をもたない３次元ローレンツ多様体の例であるウォーカー多様体の調和写像論および部分多様体論に着手した。第一歩としてウォーカー多様体の測地線と磁場軌道の部分的な分類結果を得た（Erjavec氏との共著論文を準備中）。（４）３次元ベルジェ球（Berger sphere）の標準的な接触構造に関する磁場軌道の等質性を証明した（Munteanu氏との共著論文を準備中）。（５）これらの研究の派生的な研究成果として３次元佐々木空間形の等質リーマン構造の分類に成功した（大野優氏との共著論文を準備中）。研究成果（４）に関し、研究発表（口頭発表）を行った。
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 23K03081 - Construction of harmonic maps into hyperbolic space and applications to surface theory in homogeneous spaces
Grants-in-Aid for Scientific Research
Apr. 2019 - Mar. 2023
井ノ口順一
本研究の主要課題である「調和写像の構成と等質空間内の曲面論への応用」に関し、等質空間の幾何学の観点から研究を遂行し以下の研究成果を得た。
（１）前年度に得た、双曲平面Hに値をもつ「1径数変換群の作用で同変的な調和写像」を用いた３次元ハイゼンベルグ群内の「対称性を備えた極小曲面」の構成法（Dorfmeister氏、小林氏との共同研究）に関し、具体例の詳細な記述を得ることに成功した。（３）Hと数直線の直積空間HXRの軌道型グラスマン幾何に関する前年度の研究成果と調和写像の関連を深めるために新たな研究視点と手法を導入した。Hを複素部分多様体として含む４次元等質空間（サーストン幾何の４次元類似）である2種の空間Sol40およびSol41の曲線論と曲面論を創始した（部分多様体論は未開であった）。調和写像の伝統的構成法である「極小部分多様体の構成」に着手した。極小部分多様体を複素構造の観点から構成し、いくつかの設定下で分類した（Erjavec氏との共著論文投稿中）。さらにJ-軌道（磁場軌道に相当）を分類した。（３）リー球面幾何学の建築構造設計への応用に関する研究成果を国際会議論文として発表した（横須賀氏、大崎氏、本間氏との共著）（４）(1)から(3)の研究過程において、情報幾何学への予期せぬ応用が発見された。正規分布のなす統計多様体に指定される甘利-Chentsov接続は数理統計学に由来するものであり、微分幾何学的な意味、必然性は未解明であった。正規分布のなす統計多様体を統計リー群として実現することによりある種の対称性をもつ唯一の線型接続であることを証明した（古畑氏、小林氏との共著論文を発表）（５）前年度に行った3次元佐々木空間形における磁場軌道の分類を論文発表した（Munteanu氏との共著）。Munteanu氏との検討を継続し、一般の奇数次元への拡張に成功した（共著論文を投稿中）
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), University of Tsukuba, Principal investigator, Competitive research funding, 19K03461 - Theoretical Analysis on Trimmed Surface Connection and Generation of high-quality Trimmed Surface from Measured Point Data
Grants-in-Aid for Scientific Research
01 Apr. 2019 - 31 Mar. 2022
Miura Kenjiro T.
Free-form surfaces used in automobile exterior design are required to be smooth, beautiful and of high quality. Although there is a strong need in practice, little theoretical research has been done on trimmed surfaces. So, first, as a reverse engineer for the exterior of automobiles using a trim curved surface. A least squares approximation was performed, a quadrilateral surface was fitted, and the trimmed surface was trimmed to generate a trimmed surface. Furthermore, we have researched and developed a method for fitting a tangent plane and a trimmed surface that satisfies the curvature continuity to the triangular mesh data, and succeeded in making the tangent plane of the trimmed surface and the curvature continuous.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Shizuoka University, 19H02048 - A construction of the thery of homogeneous surfaces in Riemannian symmetric spaces
Grants-in-Aid for Scientific Research
01 Apr. 2016 - 31 Mar. 2021
Naitoh Hiroo
This research is positioned as the initial research of a research project that considers the classification of homogeneous submanifolds in the Riemannian symmetric spaces from the viewpoint of the Grassmann geometry of submanifolds, and
the target submanifolds are limited to surfaces. The results obtained in this research led to the construction of a general theory regarding the framework of the Grassmann geometry of surfaces, and as a related research, gave the completion of the surface theory of Grassmann geometry in the three-dimensional Riemannian homogeneous space.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Yamaguchi University, 16K05133 - Development and Extension of Discrete Integrable Geometry
Grants-in-Aid for Scientific Research
01 Apr. 2016 - 31 Mar. 2020
Kajiwara Kenji
Discrete integrable differential geometry and its application have been studied, focusing on the integrable structure behind the discrete geometric objects. We have obtained the results on the discrete surfaces/curves and their deformation theory, discrete holomorphic functions, construction of discrete models of curves/surfaces, and stable and precise numerical method for the surfaces and interfaces. In particular, regarding the discrete surfaces/curves and their deformation theory, we formulated a good framework for the log-aesthetic curves developed in the area of the industrial design by using the Klein geometry and succeeded in generalization. Based on those results, we have proposed a project for JST CREST aiming at the development to the various areas of design, which has been successfully accepted.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Kyushu University, 16H03941 - Construction of harmonic maps into non-compact symmetric spaces via loop groups and applications to surface theory
Grants-in-Aid for Scientific Research
Apr. 2015 - Mar. 2019
Inoguchi Jun-ichi
We gave a loop group method for constructing minimal surfaces with symmetry in the 3-dimensional Heisenberg group (the model space Nil of nilgeometry in the sense of Thurston). We also established loop group methods for constructing constant negative Gaussian curvature surfaces in the hyperbolic 3-space and maximal surfaces in the 3-dimensional anti de Sitter space-time. In addition, we generalized the Uhlenbeck-Segal theory for harmonic maps into compact semi-simple Lie groups (principal chiral models) to affine harmonic maps into general Lie groups equipped with natural bi-invariant torsion free connection.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), University of Tsukuba, Principal investigator, Competitive research funding, 15K04834 - Applied analysis by discrete integrable systems and discrete differential geometry
Grants-in-Aid for Scientific Research
01 Apr. 2011 - 31 Mar. 2015
KAJIWARA Kenji; INOGUCHI Jun-ichi; NAKAYASHIKI Atsushi; MASUDA Tetsu; OHTA Yasuhiro; MATSUURA Nozomu
By applying the theory of discrete integrable systems, studies on good discretization of geometric objects such as curves and surfaces have been carried out. The main results are as follows: (1) Discrete curve theory. Development of deformation theory of plane and space discrete curves and construction of explicit formula in terms of the tau functions. (2) Theory of discrete analytic functions. Construction of explicit formula for the discrete power function in terms of hypergetomtric tau function of the Painleve VI equation and generalization. (3) As an application, systematic construction of stable and highly accurate numerical scheme for nonlinear wave phenomena in terms of self-adaptive moving mesh scheme based on discretization of the Euler-Lagrange transformation.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Kyushu University, 23340037 - Research on classical differential geometry from modern view points and its applications
Grants-in-Aid for Scientific Research
01 Apr. 2010 - 31 Mar. 2015
KUROSE Takashi; SUYAMA Yoshihiko; HAMADA Tatsuyoshi; KAWAKUBO Satoshi; MATSUURA Nozomu; INOGUCHI Junichi; FURUHATA Hitoshi; FUJIOKA Atsushi
In this research program, classical differential geometry, geometry of curves, surfaces and hypersurfaces in various spaces, have been studied, mainly with the method of the theory of integrable systems. Many results on classical differential geoemtry and its application have been achieved; for instance, through the observation that certain sorts of changes with time of curves yield equations dealt with in the theory of integrable systems, geometric descriptions and/or interpretations of several accomplishments of the theory have been given. Moreover, by applying geometry of hypersurfraces in affine spaces, new properties of statistical manifolds, which appear in informtion geometry, the study of mathematical statistics and information theory with differential geometric tools and methods, have been obtained and the statistical manifolds satisfying some curvature condition have been explicitely constructed and classified.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 22540107 - Construction of surfaces in homogeneous spaces via spin geometry and loop groups
Grants-in-Aid for Scientific Research
Apr. 2012 - Mar. 2015
INOGUCHI JUN-ICHI
We showed that constancy of Gauss curvature of surfaces (of Gauss curvature less than 1) in the 3-sphere is characterized by the harmonicity of normal Gauss map. Based on this characterization, we established a loop group method for constructing negative constant Gauss curvature surfaces and surfaces of constant positive Gauss curvature (less than 1) in the 3-sphere simultaneously. We also obtain a loop group method for constructing surfaces of constant negative Gauss curvature (greather than -1) in hyperbolic 3-space. By combining spin geometry and loop group theory , we established a loop group method for constructing minimal surfaces in the 3-dimensional Heisenberg group. As an application, we give some new examples of minimal surfaces in the Heisenberg group.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Yamagata University, Principal investigator, Competitive research funding, 24540063 - Global construction of constant mean curvature surfaces in terms of contact geometry and loop groups
Grants-in-Aid for Scientific Research
Apr. 2009 - Mar. 2012
INOGUCHI Jun-ichi
We showed that minimal surfaces in hyperbolic 3-space are obtained as projections of f-holomorphic curves in the semi-Riemannian homogeneous contact space SL(2,C)/U(1). By using the appropriate loop group splitting, for any prescribed potential, we can construct f-holomorphic curves in SL(2,C)/U(1). It is shown that non-minimal constant mean curvature surfaces with mean curvature less than 1 can be obtained from f-holomorphic curves. By using this loop group method (new DPW-method), we constructed radially symmetric constant mean curvature surfaces in hyperbolic 3-space. We classified minimal translation surfaces in the 3-dimensional Heisenberg group.
日本学術振興会, Grant-in-Aid for Scientific Research (C), Yamagata University, Principal investigator, Competitive research funding, 21540067 - New development of harmonic maps
Grants-in-Aid for Scientific Research
2009 - 2012
URAKAWA Hajime; ICHIYAMA Toshiyuki; ITOH Jinichi; OBATA Nobuaki; INOGUCHI Junichi; HIAI Fumio
In 1986, the concept of the bi-harmonic map which is an extension of harmonic maps was introduced. We raised the new notion of the bi-Yang-Mills field, which is an analog of the bi-harmonic map, and showed its isolation phenomena. That is, bi-Yang-Mills fields with some square-integral norm over compact manifolds with positive Ricci curvature must be Yang-Mills fields. We showed bi-harmonic maps which have a bounded square-integral norm must be harmonic if the target space has non-positive curvature. We classified all the bi-harmonic maps for cases where the target space is a compact Lie group or compact symmetric spaces.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Tohoku University, 21540207 - Research on constructions of constant mean curvature surfaces in terms of conformal geometry and loop groups
Grant-in-Aid for Scientific Research(C)
Apr. 2006 - Mar. 2009
INOGUCHI Jun-ichi
2 次複素特殊線型群 SL(2,C)のループ群を用いて5次元等質空間 SL(2,C)/U(1)に値をもつルジャンドル調和写像に対するループ群論的構成法(DPW 法)を確 立した。ルジャンドル調和写像と3次元双曲空間内の平均曲率一定曲面との対応により、ルー プ群論的構成法を用いて、3次元双曲空間内の、指定された臍点をもち、平均曲率が一定値で、 その絶対値が1未満の曲面を局所的に構成することが可能になった。また極小曲面も同時に構 成することが可能になった。
日本学術振興会, Grant-in-Aid for Scientific Research (C), Utsunomiya University, Principal investigator, Competitive research funding, 18540068 - Classical differential geometry from the modern viewpoint and its application
Grants-in-Aid for Scientific Research
2006 - 2009
KUROSE Takashi; SUAYMA Yoshihiko; HAMADA Tatsuyoshi; KAWAKUBO Satoshi; MATSUURA Nozomu; YAMADA Kotaro; INOGUCHI Junichi; FURUHATA Hitoshi
In this research, we studied classical differential geometry from modern viewpoints, such as of the theory of integral systems and of the theory of singularities ; we obtained results on various fields of classical differential geometry and their applications, in particular, the motions of curves associated with integrable systems, explicit construction and the classification of conformally flat hypersurfaces of four-dimensional space forms, real hypersurfaces of complex space forms, surfaces of three-dimensional spaces, affine differential geometry and its applications to Hessian geometry and information geometry, and so on.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Fukuoka University, 18540103 - 双曲空間内の曲面の無限次元リー群による構成の研究 研究課題
科学研究費 若手研究(B)
Apr. 2004 - Mar. 2006
井ノ口順一
1)2003年に発表した論文Minimal surfaces in 3-dimensional solvable Lie groups, Chinise Annals of Mathematics B24(2003),73-84において3次元ユークリッド空間・3次元双曲空間・双曲平面と直線の直積,これらをすべて含む3次元等質空間の2径数族を構成した。族内の空間はすべて可解リー群である。
この2経数族に属する各空間内の極小曲面に対するガウス写像の満たす積分可能条件を求めた.この積分可能条件を用いて,ガウス写像とある複素数値函数の組が極小曲面を定めるための必要十分条件である偏微分方程式系を導出した.その偏微分方程式の解から極小曲面を与える積分表示公式を与えた。この公式はユークリッド空間内の極小曲面に対するWeierstrass-Enneper公式を一般化したものである。論文:Minimal surfaces in 3-dimensional solvable Lie groups IIとしてBullentin of the Australian Mathematical society誌に掲載が決定した。
2)極小はめこみ・調和写像の拡張概念である重調和写像・重調和はめ込みの具体例の構成を研究した。3次元双曲空間・3次元ユークリッド空間には極小でない重調和曲面が存在せず,3次元球面には極小でない重調和曲面は特定の半径をもつ小球のみであることが知られている。これらの事実に立脚し,極小でない重調和曲線・重調和曲面を許容する3次元等質空間を考察した。
とくに3次元既約標準簡約等質空間内の重調和曲線を分類した。この成果はJong Taek Cho氏,Jin-Eum Lee氏との共著論文Biharmonic curves in 3-dimensional Sasakain space formsとしてAnnali di Matematica et pura Applicata誌に掲載が決定した。
日本学術振興会, 若手研究(B), 宇都宮大学, Principal investigator, Competitive research funding, 16740029 - The global behavior of curves and surfaces in space forms
Grants-in-Aid for Scientific Research
2003 - 2006
UMEHARA Masaaki; KOISO Norihito; YAMADA Kotaro; ROSSMAN Wayne F; KOKUBU Masatoshi; INOGUCHI Junichi
We get the following results :
1.A maximal surface which is given by the real part of holomorphic isotropic immersion into C^3 is called a maxface. As a joint work with K.Yamada, the head investigator Umehara gave a Weierstrass-type representation formula for maxfaces, and gave an Osserman-type ineqality for complete maxfaces. The equality holds if and only if all ends of the surfaces are properly embedded. Moreover, as a joint work with K.Saji, S.Fujimori, and K.Yamada, the head investigator Umehara gave a criterion for the cuspidal cross cap, and showed that generic singular points for maxfaces consists of cuspidal edge, swallowtail and cuspidal cross cap.
2.As a joint work with K.Saji and K.Yamada, the head investigator Umehara studied the behavior of Gaussian curvature near the cuspidal edge and the swallowtail. In particular, the new geometric invariant on cuspidal edges called the singular curvature is introduced, and show that the integration of the singular curvature on the singular set is closely related to the Euler number of the surface.
3.A curve γ in the real projective plane is called anti-convex if for each point p on the curve, there exists a line passing through the point which does not meet y other than p. As a joint work with G.Thorbergsson, the head investigator Umehara studied the inflection points on anti-convex curves, and showed that the number of inflection points I and the number of the independent double tangents D satisfies the relation I-2D=3.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Osaka University, 15340024 - Application of integrable systems methods to surfaces with particular variational properties
Grants-in-Aid for Scientific Research
2003 - 2006
ROSSMAM W.F.; OHNITA Yoshihiro; GUEST M.; YAMADA Kotaro; KOKUBU Masatoshi; INOGUCHI Jun-ichi
The following results were obtained:
1) In a joint research project with U. Hertrich-Jeromin, S. Santos and F. Burstall, a suitable definition for discrete constant mean curvature surfaces in 3 dimensional space forms was obtained. Those 3 dimensional space forms consist of Euclidean 3-space, spherical 3-space and hyperbolic 3-space. It was shown that this new definition matches the old definition that is known for the Euclidean case, and this definition is new in the hyperbolic case. Using this definition, discrete Delaunay surfaces were studied, along with their discrete Darboux and Backlund transformations. An important tool in this research was the notion of conserved quantities. The case of smooth surfaces was developed by S. Santos and F. Burstall, while the discrete case was developed by U. Hertrich-Jeromin and myself.
2) In a joint research project with my Ph.D. graduate student N. Sultana, the stability and Morse index of constant mean curvature surfaces of revolution in spherical 3-space was studied. Because the axis of such a surface is a closed loop, these surfaces can become close tori, and then they will have finite index. It was shown that all such surfaces are unstable, and that they all have index at least 5, and (depending on the choice of surface) the index can be arbitrarily large. The index is the number of negative eigenvalues of the associated Jacobi operator.
3) In a continuation of a project with M. Kokubu, M. Umehara and K. Yamada, surfaces with constant Gauss curvature 0 in hyperbolic 3-space (flat fronts, which can have singularities) were studied. In particular, this year, it was shown that the caustics of such surfaces can have ends with asymptotic behavior described by cycloids.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Kobe University, 15340023 - Classical differential geometry from the modern viewpoint and its applications
Grants-in-Aid for Scientific Research
2003 - 2005
KUROSE Takashi; SUYAMA Yoshihiko; HAMADA Tatsuyoshi; YAMADA Kotaro; INOGUCHI Jun-ichi; FURUHATA Hitoshi
In this research, we planned to give a now development of the theories of classical differential geometry by restructuring them from the modern viewpoint, particularly, of the theories of integrable systems and of singularities. Our main results are the following :
1.(1)In affine differential geometry, one of the core theories of classical differential geometry, we mainly studied the geometry of affine hyperspheres and their representation formulae, and showed a relationship with the geometry of holomorphic statistical manifolds and the several properties of the center maps. We also studied the discretization of affine or centroaffine plane curves and gave a description of their time-evolution following discrete soliton equations ; (2)we characterized the classical examples of conformally flat hypersurfaces in 4-dimensional Euclidean space and constructed new examples ; (3)for real hypersurfaces in complex space forms, we introduced a new geometric invariant and classified Hopf real hypersurfaces using the invariant.
2.We studied the geometric properties of surfaces with singularities and obtained the following results : (1)We constructed the theory of flat fronts, the flat surfaces with singularities of a certain kind in 3-dimensional hyperbolic space. In particular, we defined (weak) completeness of flat fronts and showed their global properties ; (2)investigating the properties of the singularities of maximal surfaces in 3-dimensional Minkowski space, we constructed the theory of maxfaces, the spacelike maximal surfaces allowing singularities of a certain kind.
3.We studied transformations of surfaces and showed that the transformations given by the sphere congruences in Moebius geometry are obtained by the complexified line congruences in Euclidean space. We also investigated biharmonic curves in 3-dimensional homogeneous spaces and determined such curves when the homogeneous spaces are irreducible and reductive.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Fukuoka University, 15540100 - Geometry of the flat tori in the sphere and non- linear wave equations
Grants-in-Aid for Scientific Research
2003 - 2005
KITAGAWA Yoshihisa; SAKAI Kazuhiro; INOGUCHI Jun-ichi; AIHARA Yoshihiro
In this research, we studied geometry of flat tori in the 3-sphere, meromorphic mappings, surfaces of constant mean curvature and dynamical systems. The main results of this reseach are summarized as follows.
1.Studies on flat tori in the 3-sphere. In this research, Y.Kitagawa studied the conjecture that any isometric deformation of compact surface in $S^3$ preserves the enclosed volume.
As a result, he proved that the conjecture is ture for all flat tori in $S^3$.
2.Studies on meromorphic mappings. In this research, Y.Aihara proved that for every hypersurface $D$ of degree $d$ in a complex projective space, there exists a holomorphic curve from the complex plane into the projective space whose deficiency for $D$ is positive and less than one.
3.Studies on constant mean curvature surfaces and Backlund transformations. In this research, J.Inoguchi proved that Bianchi-Backlund transformation of a constant mean curvature surface is equivalent to the Darboux transformation and the simple type dressing.
4.Studies on dynamical systems. In this research, K. Sakai proved that the $C^1$ interior of the set of expansive vector fields on a manifold is characterized as the set of vector fields without singularities satisfying both Axiom A and the quasi-transversality condition.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Utsunomiya University, 15540059 - Generalizations of Weierstrass-type representation formulae and applications
Grants-in-Aid for Scientific Research
2002 - 2005
YAMADA Kotaro; MIYAOKA Reiko; SAEKI Osamu; UMEHARA Masaaki; KUROSE Takashi; TAKAHASHI Masaro
1.W rewrote the Weierstrass-type representation formula for flat surfaces in hyperbolic 3-space in the form without integration (Darboux-type formula), and classified complete flat surfaces with small numbers of ends. 2.We pointed out the class of ambient spaces for which an analogue of Weierstrass-type (Bryant) representation formula for mean curvature one surfaces in hyperbolic 3-space holds. 3.We found criteria for singularities (cuspidal edges, swallowtails, cuspidal cross caps) which are generic singularities of fronts or frontals. 4.We established fundamental notions of flat fronts in hyperbolic 3-space, and investiagted properties of singularities of such surfaces. 5.We defined a certain class of maximal surfaces with singularities in Minkowski 3-space (called maxface), and investigated their singularities.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Kyushu University, 14340024 - 定曲率空間内の曲面の無限次元リー群による構成の研究
科学研究費助成事業
2002 - 2003
井ノ口 順一
3次元定曲率空間内の「可積分系構造を持つ曲面」を無限次元リー群論的に構成する研究を継続して行なった。本年度は平均曲率一定曲面の変換論を小林真平氏(神戸大学・ミュンヘン工科大学)と共同で研究した。3次元ユークリッド空間内の平均曲率曲面は線叢による変換(Backlund変換)を許容しない。19世紀にL.Bianchiは線叢の複素化を考察し平均曲率一定曲面から新たな平均曲率一定曲面を得る操作を得た。この操作をBianchi-Backlund変換(BB変換)とよぶ。自明解である円柱面にBB変換を施して得られる平均曲率一定曲面をバブルトン(bubbleton)と呼ぶ。一方、平均曲率一定曲面は双等温曲面(isothermic surface)の典型例である。双等温という性質は共形変換で不変であり「共形幾何における球叢」を用いた変換論が展開できる。球叢による双等温曲面の変換はDarboux変換とよばれる。Darboux変換は複素一径数に依存する。複素一径数は実または準虚数でなければならない。
1997年に出版された論文でUdo Hertich-JerominとFranz Peditは「平均曲率一定曲面に対するDarboux変換で実一径数に依存するものはBianchi-Backlund変換と一致すること」を示した。更に次の予想を提出した。"純虚数に依存するDarboux変換はBB変換に由来しないであろう"
(1)複素線叢を詳細に再検討し変換にはもう一種,「平均曲率一定曲面の変換」を与えるものがあることを発見した。
(2)従来の研究において漏れていたBB変換は「純虚数型のDarboux変換」であることを示した。
以上2つの研究結果によりHertrich-Jeromin・Peditの予想に対し否定的解答を与えた。
(論文:Shimpei Kobayashi and Jun-ichi Inoguchi,"Another bubbletons"として発表予定.2003年7月の国際会議で口頭発表)今年度の成果は従来から期待されている複素ドレッシング変換論構築への道標に相当することから注目を浴びている。
日本学術振興会, 若手研究(B), 宇都宮大学, 14740053 - Modern Research of Affine and Projective Geometry and its Applications
Grants-in-Aid for Scientific Research
2000 - 2002
KUROSE Takashi; YAMADA Kotaro; HAMADA Tatsuyoshi; SUYAMA Yoshihiko; FURUHATA Hitoshi; INOGUCHI Jun-ichi
In this research, we studied classical differential geometries, theory of integral systems and information geometry.
1. Classical Differential Geometries (1) We characterized minimal affine hypersurfaces and minimal centroaffine immersions of codimension two. Moreover, we gave an explicit method of constructing self-dual minimal centroaffine surfaces of codimension two.
(2) We studied manifolds with projectively flat torsion-free affine connection whose Ricci curvature is symmetric and definite, and showed fundamental results on the injectivity of the projective developing maps of such manifolds and the convexity of their image.
(3) For conformally flat hypersurfaces of a 4-dimensional sphere, we defined a new conformal invariant. Using the invariant, we characterized the classical examples and constructed new examples.
(4) We developed a very concrete and comprehensive theory on curves and surfaces in 3-dimensional homogeneous spaces.
2. Integrable Systems We investigated various integrable systems appeared in classical differential geometries. We obtained representation formulae for minimal surfaces in 3-dimensional solvable Lie groups and flat surfaces in a 3-dimensional hyperbolic space. We also developed a comprehensive theory of (spacelike) surfaces with harmonic inverse mean curvature in 3-dimensional Riemannian space forms and Lorentzian space forms.
3. Information Geometry and Statistical Manifolds (1) We defined complex statistical manifolds and studied them from the view points of affine differential geometry and of information geometry, especially of quantum estimation theory.
(2) As a generalization of special Kahler manifolds, we defined statistical manifolds with compatible complex structure and investigated their fundamental properties.
(3) On (-1)-conformally flat statistical manifolds, we gave an explicit method of constructing the Volonoi diagrams.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Fukuoka University, 12640097 - 定曲率空間内の曲面に対する無限次元群作用の研究
科学研究費助成事業
2000 - 2001
井ノ口 順一
前年度に引き続きBacklund変換の変換群論的把握に向けて無限次元リー群論の観点から研究を行った。また対称空間ではない等質空間内の曲面・調和写像の構成についても研究を行った。
(1)Chaohao Gu氏(谷超豪),Hesheng Hu氏(胡和生)(中国・Fudan University)と共同研究を行い以下の成果を得た。
Liouville方程式・cosh-Gordon方程式に対するBacklund変換を与えた。さらにこれらのBacklund変換を負定値計量をもつ3次元空間(ミンコフスキー空間)内の時間的曲面間の空間的線叢および時間的線叢として幾何学的に定義できることを示した。
上述のBacklund変換を「フレームに対する変換」として再定式化しループ群論的解釈を与えた。
2)J.Dorfmeister, F.Pedit, H.Wuによる「リーマン面からコンパクト・リーマン対称空間への対称空間」に対するループ群論的WeierstraB構成法(非線型ダランベール公式)を対称ではない標準簡約等質空間(naturally reductive homogeneous space)への拡張を研究した。その成果として実Stiefel多様体への水平的調和写像に対しWeierstraB構成法が適用できることがわかった。この成果は3次元定曲率空間内の平均曲率一定曲面の構成に応用できる。
(3)3次元ユークリッド空間内の極小曲面に対するWeierstraB-Enneper表現公式を3次元可解リー群に対し拡張した。この拡張版の公式は國分雅敏氏による「3次元双曲空間内の極小曲面に対する表現公式」をも含む。
(4)実特殊線型群SL(2,R)内の平均曲率一定曲面のガウス写像の調和性を研究した。とくに平均曲率一定曲面でガウス写像が鉛直調和(vertically harmonic)である曲面を分類・決定した。さらに平均曲率一定曲面でガウス写像が調和となるものを分類・決定した。
(5)Mohamed Belkhelfa氏,Franki Dillen氏(KU Leuven,ベルギー)と共同研究を行い3次元標準簡約等質空間(naturally reductive homogeneous space)内の第二基本形式が平行な曲面を分類・決定した。
日本学術振興会, 奨励研究(A), 福岡大学, 12740051 - Applications of integrable systems in geometry and topology
Grants-in-Aid for Scientific Research
2000 - 2001
GUEST Martin; KAMISHIMA Yoshinobu; OKA Mutsuo; OHNITA Yoshihiro; INOGUCHI Junichi; UDAGAWA Seiichi
Results were obtained on the geometry and topology of harmonic maps and spaces of harmonic maps, especially in the case where the domain is a Riemann surface and the target space is a compact Lie group or symmetric space. Guest used a generalization of the Weierstrass representation for minimal surfaces to study harmonic maps from the two-dimensional sphere (or, more generally, harmonic maps of finite uniton number, from any Riemann surface) to the unitary group. Earlier results of Uhlenbeck, Segal, Dorfmeister-Pedit-Wu, Burstall-Guest were developed into an effective tool for describing such maps. In particular, an explicit canonical form was obtained, and this was used to study the space of all such maps. The main application was a description of the connected components of the space of harmonic maps from the two-dimensional sphere to the unitary group. Ohnita used a different approach, based on earlier work of Hitchin in gauge theory, to obtain a framework for studying the geometry (in particular, the pre-symplectic geometry) of spaces of harmonic maps.
The harmonic map equation can be regarded as an integrable system, and the above work sheds light on other integrable systems. Two other examples of integrable systems were studied from this point of view, and preliminary results obtained. The first example, studied by Guest, was the theory of quantum differential equations. Parallels with harmonic maps were established, forming the basis for future work in this direction. Results on quantum cohomology of symmetric spaces were obtained also by Ohnita and Nishimori, and on quantum cohomology of flag manifolds by Guest and Otofuji. The second example, studied by Burstall and Calderbank, was the integrable systems aspect of conformal and Mobius geometry, and a new approach was initiated.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Tokyo Metropolitan University, 12640083 - Geometry of surfaces in space forms
Grants-in-Aid for Scientific Research
1999 - 2000
UMEHARA Masaaki; HONDA Nobuhiro; KANNO Hiroaki; MATSUMOTO Takao; INOGUCHI Junichi; KOKUBU Masatoshi
We get the following results :
1. The head investigator Umehara gave a classification for complete constant mean curvature 1 surfaces (i.e. CMC-1 surfaces) in the hyperbolic 3-space H^3 of total absolute curvature (resp. the dual total absolute) curvature less than or equal to 4π. Moreover, he gave non-existence and existence results when the surfaces has dual total curvature less than or equal to 8π. These results are shown in a joint work with Rossman and Yamada.
2. The head investigator Umehara, Kokubu, Takahashi and Yamada gave a theory of surfaces with holomorphic Gauss maps in the duals of compact semisimple Lie groups, which is a generalization of CMC-1 surfaces in H^3, and show an analogue of Chern-Osserman Inequality for minimal surfaces in the Euclidean π-space. Moreover, they gave several non-trivial examples of such surfaces and showed mean curvature of these surfaces are all proportional to the sectional curvature of the ambient space.
3. The head investigator Umehara and Bobenko investigated the monodromy of constant mean curvatures in H^3 and showed that the number of isometric immersions with a prescribed constant mean curvature into H^3 on a given Riemannian 2-manifold is finite.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hiroshima University, 11640080 - Research for manifolds with conformal structure
Grants-in-Aid for Scientific Research
1997 - 1999
SUYAMA Yoshihiko; KUROSE Takashi; AKUTAGAWA Kazuo; SHIOHAMA Katsuhiro; INOGUCHI Jun-ichi; YAMADA Kataro
1. Conformably flat hypersurfaces. We studied conformally flat, hypersurfaces in the space forms of dimension 4, and found a good structure on the 4-dimensional standard sphere for each hypersurface. According to the structure, the set of conformally flat hypersurfaces is divided into three classes : the parabolic class, the elliptic class, and the hyperbolic class. We showed that the classes are invariant under conformal transformations of the sphere and the respective class consists of conformally flat hypersurfaces constructed by surfaces of constant curvature in one of the 3-dimensional space forms : the Euclidean space, the hyperbolic space, or the sphere.
2. Conformal-projective transformations of statistical manifolds. In this study, we obtained the following result : A conformal-projective transformation of a statistical manifold leaves all umbilical points and the skew-symmetric component of the Ricci curvature of any hypersurfaces ; moreover, this property characterizes the conformal-projective transformations when the dimension of the statistical manifold is greater than 2. We also found a tensor field that is invariant under any conformal-projective transformations and that reduces to the conformal curvature tensor if the underlying statistical manifold is a usual Riemannian manifold.
3. A representation formula of surfaces with constant mean curvature (CMC surfaces) in a 3-dimensional space form and their Gauss map. The existence problem of harmonic maps was studied in the case where the destination is a non-complete Riemannian space with non-positive curvature unbounded from below. In this situation, we showed tile existence and the uniqueness theorems of harmonic maps for a Dirichlet problem at infinity. As an application, we constructed CMC surfaces in the 3-dimensional hyperbolic space form.
4. An extension of the class of CMC surfaces from the viewpoint of the theory of integrable systems. We defined surfaces with harmonic inverse mean curvature (HIMC surfaces) in the 3-dimentional space forms, and showed that there exists a correspondence among the HIMC surfaces similar to the Lawson correspondence, one of the features of the class of CMC surfaces. We also studied the relation between the class of HIMC surfaces and the class of H-surfaces, which is an extension of the class of CMC surfaces from the variational viewpoint. As a result, we proved that HIMC surfaces are obtained from the gauge-theoretic equation for H-surfaces with a certain condition of reduction.
Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), FUKUOKA UNIVERSITY, 09440044
Social Contribution Activities
- 高等学校の幾何学とは?
14 Feb. 2026
Lecturer
高校数学教育を楽しく考えよう!の会
2025年度公開研究会「高等学校数学科における《実験数学》と探究活動の授業開発の紹介」
沖縄県教育福祉会館
Teachers - 現代数学とはなにか。自然科学からの自立と協調
01 Nov. 2025
Lecturer
北大道新アカデミー
100年の時をこえて～「なぜ？」をつなぐ理学の継承者たち～ - 大学で学ぶ「数学」/「光る君へ」と場合の数
20 Dec. 2024
Lecturer
旭川西高等学校模擬授業 - 生徒の表現力を高める授業
07 Jun. 2019
Lecturer, Advisor
岩手県高等学校教育研究会数学部会定期総会・研修会
岩手県立生涯学習推進センター
Teachers - 三角形の内角の和は？ 模様のひみつ
07 Nov. 2018
Lecturer
茨城県立竜ヶ崎第一高等学校SSH事業 レインボー・マスマティクス5th - 深い学びを問う数学授業のあり方
16 Jul. 2017
Lecturer
岩手県高等学校教育研究会数学部会中部地区研究集会
ホテルグランシェール花巻
Teachers - 見通す力を作る授業について
25 Jul. 2016
Lecturer
岩手県高等学校教育研究会数学部会県北地区研究集会
二戸市民文化会館
Teachers - 数楽の授業をつくる．数楽コミュニケーション力
24 Jul. 2015
Lecturer
岩手県高等学校教育研究会数学部会盛岡地区研究集会
サンセール盛岡
Teachers - 学力向上をめざす授業を作る ＜体感する数学＞
25 Jul. 2014
Lecturer
岩手県高等学校教育研究会数学部会県南地区研究集会
水沢グランドホテル
Teachers - 岩手県SSH 指定校等課題研究中間発表会
19 Oct. 2013
Advisor
岩手県SSH 指定校等課題研究中間発表会
盛岡第三高等学校
High school students, Teachers - 数学授業の見える化
26 Jul. 2013
Lecturer
岩手県高等学校教育研究会数学部会沿岸地区研究集会
岩手県立釜石商工高等学校
Teachers - どこにでも居る幾何．アサガオから宇宙まで
13 Jun. 2013
Lecturer
栃木県県立足利高等学校SSH講演会
High school students - 数学を研究してみよう
20 Oct. 2012
Lecturer
岩手県立盛岡北高等学校
High school students - 見て・触って・感じる数学
23 Oct. 2011
Lecturer
山形県立博物館
Schoolchildren, Junior high school students, High school students, College students, Graduate students, Teachers, Guardians, General - 授業における魅力ある教材作りについて
14 Sep. 2011
Lecturer
山形市中学校教育研究会数学部会研修会
山形市立第三中学校
Teachers - 数学は文科（文化）と理科（科学）をつなぐことば
11 Feb. 2011
Lecturer
山形大学理学部「科学文化の拠点形成＠やまがた」プロジェクトシンポジウム
山形県立図書館遊学館
General - すうがくのはなし（形のひみつ）
21 Oct. 2009
Lecturer
山形県立酒田西高等学校
High school students - 形の数学
24 Aug. 2006
Lecturer
宇都宮女子高校（会場：宇都宮大学）
High school students - あなたの知らない数学の世界！
07 Oct. 2005 - 21 Oct. 2005
Lecturer
宇都宮大学生涯学習教育研究センター公開講座
High school students, College students, General - 数学科教材開発論
04 Jun. 2004 - 12 Jun. 2004
Lecturer
宇都宮大学教育職員免許法認定講習公開講座
Teachers - あなたは知らない本物の数学. 数学嫌いになるのはちょっと待って！
15 May 2004 - 29 May 2004
Lecturer
宇都宮大学生涯学習教育研究センター 公開講座
High school students, General - 栃木県教育職員免許法認定講習（幾何学）
05 Aug. 2003 - 06 Aug. 2003
Lecturer
栃木県教育委員会
Teachers - せめる算数・数学教育
09 Aug. 2002
Lecturer
栃木県算数数学教育同好会
栃木県総合文化センター
Teachers
