Researcher Profile and Settings

Affiliation

• Faculty of Science　Mathematics　Mathematics

Job Title

• Professor

Research funding number

• 40309886

J-Global ID

• 200901040204658633

Research Interests

• Integrable Systems   loop group   harmonic map   minimal surface   CMC surface   DPW-method   contact structure   spin structure   magnetic harmonic map   Differential Geometry   Discrete Differential Geometry   

Research Areas

• Natural sciences / Geometry

Academic & Professional Experience

• 2022/10 - Today Hokkaido University Graduate School of Science
• 2015/04 - 2022/09 University of Tsukuba

Association Memberships

• 日本数学会   THE SOCIETY FOR SCIENCE ON FORM, JAPAN   The Japan Society for Industrial and Applied Mathematics   

Research Activities

Published Papers

• 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 2023/11 [Refereed]
  
• J-trajectories in 4-dimensional solvable Lie Group $\mathrm{Sol}_1^4$

  Zlatko Erjavec, Jun-ichi Inoguchi

  Journal of Nonlinear Science 33 (6) 0938-8974 2023/09/25 [Refereed]
  
• Characteristic Jacobi operator on almost Kenmotsu $3$-manifolds

  Jun-ichi Inoguchi

  International Electronic Journal of Geometry 16 (2) 464 - 525 2023/09/22 [Refereed]
   

  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 0167-8396 2023/09 [Refereed]
  
• Minimal submanifolds in $\mathrm{Sol}_1^4$

  Zlatko Erjavec, Jun-ichi Inoguchi

  Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 117 (4) 1578-7303 2023/08/22 [Refereed]
  
• Contact 3-manifolds with pseudo-parallel characteristic Jacobi operator

  Jun-ichi Inoguchi, Ji-Eun Lee

  Mediterranean Journal of Mathematics 20 (5) 1660-5446 2023/08/05 [Refereed]
  
• Minimal submanifolds in $\mathrm{Sol}_0^4$

  Zlatko Erjavec, Jun-ichi Inoguchi

  The Journal of Geometric Analysis 33 (9) 1050-6926 2023/06/16 [Refereed]
  
• Killing magnetic curves in $\mathbb{H}^{3}$

  Zlatko Erjavec, Jun-ichi Inoguchi

  International Electronic Journal of Geometry 2023/04/16 [Refereed]
   

  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 0219-8878 2023/04/07 [Refereed]
  
• Killing submersions and magnetic curves

  Jun-ichi Inoguchi, Marian Ioan Munteanu

  Journal of Mathematical Analysis and Applications 520 (2) 126889 - 126889 0022-247X 2023/04 [Refereed]
  
• 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) 1578-7303 2023/02/20 [Refereed]
  
• Magnetic Jacobi fields in Sasakian space forms

  Jun-ichi Inoguchi, Marian Ioan Munteanu

  Mediterranean Journal of Mathematics 20 (1) 1660-5446 2022/12/11 [Refereed]
  
• 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 2022/11/15 [Refereed]
   

  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 SPRINGER BASEL AG 113 0047-2468 2022/06/28 [Refereed]
   

  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 WORLD SCIENTIFIC PUBL CO PTE LTD 19 (8) 0219-8878 2022/06 [Refereed]
   

  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) 2022/05 [Refereed]
   

  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.
• アフィン接続と接触構造に関する話題から

  井ノ口, 順一

  Geometry and Analysis Fukuoka 11 - 34 2022/03 [Not refereed]
  
• J-trajectories in 4-dimensional solvable Lie group Sol_0^4

  Erjavec, Zlatko, Inoguchi, Jun-ichi

  Mathematical Physics, Analysis and Geometry 25 2022/03 [Refereed]
  
• Magnetic Jacobi fields in 3-dimensional Sasakian space forms

  Inoguchi, Jun-ichi, Munteanu, Marian Ioan

  The Journal of Geometric Analysis SPRINGER 32 (3) 1050-6926 2022/03 [Refereed]
   

  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 International Association for Shell and Spatial Structures (IASS) 821 - 833 2021/06 [Refereed]
  
• 𝜖𝜅 -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 Springer 38 (8) 2723 - 2738 0178-2789 2021/05 [Refereed]
   

  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.
• 魅力的な曲線たちー拡がりゆく可積分幾何・差分幾何ー

  井ノ口 順一

  SUGAKU 社団法人 日本数学会 73 (1) 88 - 103 0039-470X 2021/01 [Refereed]
  
• A characterization of the alpha-connections on the statistical manifold of normal distributions

  Furuhata, Hitoshi, Inoguchi, Jun-ichi, Kobayashi, Shimpei

  Information Geometry SPRINGER 4 177 - 188 2511-2481 2020/10 [Refereed]
  
• The Gauss maps of Demoulin surfaces with conformal coordinates

  Inoguchi, Jun-ichi, Kobayashi, Shimpei

  Science China Mathematics SPRINGER 64 (7) 1479 - 1492 1674-7283 2020/10 [Refereed]
   

  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 International Press 23 (8) 2161 - 2205 1095-0761 2020/05 [Refereed][Not invited]
   

  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 公益社団法人 精密工学会 2019 872 - 873 2019/09 [Not refereed][Not invited]
   

  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．
• 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 公益社団法人 精密工学会 2019 872 - 873 2019/09 [Not refereed][Not invited]
   

  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 Oxford University Press 4 (1) 2019/06 [Refereed][Not invited]
  
• Grassmann geometry on the 3-dimensional non-unimodular Lie groups

  Inoguchi, Jun-ichi, Naitoh, Hiroo

  Hokkaido Mathematical Journal HOKKAIDO UNIV, DEPT MATHEMATICS 48 (2) 385 - 406 0385-4035 2019/06 [Refereed][Not invited]
   

  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.
• Generalization of log-aesthetic curves via similarity geometry

  Inoguchi, Jun-ichi, Ziatdinov, Rushan, Miura, Kenjiro T

  Japan Journal of Industrial and Applied Mathematics Springer Japan 36 (1) 239 - 259 0916-7005 2019/01 [Refereed][Not invited]
   

  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 𝐺𝑛 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 IOP Publishing home 2 (11) 2399-6528 2018/11 [Refereed][Not invited]
   

  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.
• 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 2018/08 [Not refereed][Not invited]
   

  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 京都大学数理解析研究所 2071 1 - 16 2018/04 [Not refereed][Not invited]
   

  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 1686-4360 2018/03/04 [Refereed][Not invited]
   

  A curve is considered fair if it consists of continuous and few monotonic curvature segments. Polynomial curves such as Bézier and B-spline curves have complex curvature function, hence the curvature profile may oscillate easily with a little tweak of control points. Thus, bending energy and shear deformation energy are common fairness metrics used to produce curves with monotonic curvature profiles. The fairness metrics are used not just to evaluate the quality of curves, but it also aids in reaching to the final design. In this paper, we propose two types of fairness metric functionals to fair plane curves defined by the similarity geometry invariants, i.e. similarity curvature and its reciprocal to extend a variety of aesthetic fairing metrics. We illustrate numerical examples to show how log-aesthetic curves change depending on σ and G1 constraints. We extend LAC by modifying the integrand of the functionals and obtain quasi aesthetic curves. We also propose σ-curve to introduce symmetry concept for the log-aesthetic curve.
• 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 0167-8396 2018/03/01 [Refereed][Not invited]
   

  In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler–Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae.
• 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 2018/03 [Not refereed][Not invited]
  
• 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 - 九州大学応用力学研究所 29AO-S7 61 - 68 2018/03 [Refereed][Not invited]
   

  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．
• 19世紀の微分幾何

  井ノ口, 順一

  津田塾大学 数学・計算機科学研究所報 津田塾大学 38 (38) 68 - 80 2017/03 [Not refereed][Not invited]
  
• Periodic magnetic curves in Berger spheres

  Jun-Ichi Inoguchi, Marian Ioan Munteanu

  Tohoku Mathematical Journal 69 (1) 113 - 128 0040-8735 2017/03/01 [Refereed][Not invited]
   

  It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe it. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criterion for periodicity of magnetic curves on the unit sphere S3.
• Finite gap solutions for horizontal minimal surfaces of finite type in 5-sphere

  Inoguchi, Jun-ichi, Taniguchi, Tetsuya, Seiichi, Udagawa

  Journal of Integrable Systems Oxford University Press 1 (1) 2016/12 [Refereed][Not invited]
  
• 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 0001-8708 2016/08 [Refereed][Not invited]
   

  We generalize the UhlenbeckSegal theory for harmonic maps into compact semi-simple Lie groups to general Lie groups equipped with torsion free bi-invariant connection. (C) 2016 Elsevier Inc. All rights reserved.
• 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 0034-4877 2016/08 [Refereed]
  
• 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 2016/06 [Refereed][Not invited]
   

  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 0008-4395 2016/03 [Refereed]
   

  Abstract In this note we present a simple alternative proof for the Bernstein problem in the threedimensional Heisenberg group Nil₃ by using the loop group technique. We clarify the geometric meaning of the two-parameter ambiguity of entire minimal graphs with prescribed Abresch- Rosenberg diòerential.
• 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 1093-6106 2016
• dNLS Flow on Discrete Space Curves

  Sampei Hirose, Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta

  MI Lecture Note 64 93 - 102 2015/09 [Refereed][Not invited]
   

  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 Kyushu University 64 121 - 124 2188-1200 2015/09 [Not refereed][Not invited]
  
• Harmonic maps in almost contact geometry

  Inoguchi,Jun-ichi

  SUT Journal of Mathematics 50 (2) 353 - 382 0916-5746 2014/12 [Refereed][Not invited]
   

  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 0030-8730 2014/07/26 [Refereed]
  
• 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  1751-8113 2014/06 [Refereed][Not invited]
   

  In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym-Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces.
• 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 0075-4102 2014/01 [Refereed][Not invited]
   

  In hyperbolic 3-space H-3 surfaces of constant mean curvature H come in three types, corresponding to the cases 0 <= H < 1, H = 1, H > 1. Via the Lawson correspondence the latter two cases correspond to constant mean curvature surfaces in Euclidean 3-space E-3 with H = 0 and H not equal 0, respectively. These surface classes have been investigated intensively in the literature. For the case 0 <= H < 1 there is no Lawson correspondence in Euclidean space and there are relatively few publications. Examples have been difficult to construct. In this paper we present a generalized Weierstrass type representation for surfaces of constant mean curvature in H-3 with particular emphasis on the case of mean curvature 0 <= H < 1. In particular, the generalized Weierstrass type representation presented in this paper enables us to construct simultaneously minimal surfaces (H = 0) and non-minimal constant mean curvature surfaces (0 < H < 1).
• Magnetic maps

  Jun-Ichi Inoguchi, Marian Ioan Munteanu

  International Journal of Geometric Methods in Modern Physics 11 (6) 1450058  0219-8878 2014 [Refereed][Not invited]
   

  In this paper, we introduce the notion of magnetic maps between Riemannian manifolds. They are generalizations of both magnetic curves and harmonic maps. We provide some fundamental examples of magnetic maps. Furthermore, we study some classes of magnetic surfaces in Euclidean 3-space. © 2014 World Scientific Publishing Company.
• 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 [Refereed][Not invited]
  
• Contact metric hypersurfaces in complex space forms

  Jong Taek CHO, Jun-ichi INOGUCHI

  Differential Geometry of Submanifolds and its Related Topics 2013/10/29 [Refereed][Invited]
  
• 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 1673-3452 2013/10 [Refereed][Not invited]
   

  Integrable discretizations of the complex and real Dym equations are proposed. N-soliton solutions for both semi-discrete and fully discrete analogues of the complex and real Dym equations are also presented.
• 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 2013/09 [Refereed][Not invited]
   

  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 1225-1763 2012/10/31 [Refereed]
  
• MOTION AND BACKLUND TRANSFORMATIONS OF DISCRETE PLANE CURVES

  Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta

  KYUSHU JOURNAL OF MATHEMATICS Faculty of Mathematics, Kyushu University,九州大学大学院数理学研究院 66 (2) 303 - 324 1340-6116 2012/09 [Refereed][Not invited]
   

  We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms of the tau function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.
• Affine biharmonic curves in 3-dimensional homogeneous geometries

  Jun-ichi Inoguchi, Ji-Eun Lee

  Mediterranean Journal of Mathematics 10 (1) 571 - 592 1660-5446 2012/04/20 [Refereed]
  
• Minimal translation surfaces in the Heisenberg group $\mathrm{Nil}_3$

  Jun-ichi Inoguchi, Rafael López, Marian-Ioan Munteanu

  Geometriae Dedicata 161 (1) 221 - 231 0046-5755 2012/02/25 [Refereed]
  
• 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  1751-8113 2012/02 [Refereed][Not invited]
   

  We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the tau function are presented. Backlund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation.
• 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  1751-8113 2011/09 [Refereed][Not invited]
   

  We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.
• 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 2011/03 [Refereed][Not invited]
  
• Grassmann geometry on the 3-dimensional unimodular lie groups II

  Jun-Ichi Inoguchi, Hiroo Naitoh

  Hokkaido Mathematical Journal 40 (3) 411 - 429 0385-4035 2011 [Refereed][Not invited]
   

  We study the Grassmann geometry of surfaces in the special real linear group SL(2, R).
• On $\varphi$-Einstein contact Riemannian manifolds

  Jong Taek Cho, Jun-ichi Inoguchi

  Mediterranean Journal of Mathematics 7 (2) 143 - 167 1660-5446 2010/04/22 [Refereed]
  
• Grassmann geometry on the 3-dimensional unimodular Lie groups I

  Jun-ichi Inoguchi, Hiroo Naitoh

  HOKKAIDO MATHEMATICAL JOURNAL 38 (3) 427 - 496 0385-4035 2009/08 [Refereed][Not invited]
   

  We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional unimodular Lie group with left invariant metric, that is, it is one of the 3-dimensional commutative Lie group, the 3-dimensional Heisenberg group, the groups of rigid motions on the Euclidean or the Minkowski planes, the special unitary group SU(2), and the special real linear group SL(2, R).
• LIGHTLIKE SURFACES IN MINKOWSKI 3-SPACE

  Jun-Ichi Inoguchi, Sungwook Lee

  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS 6 (2) 267 - 283 0219-8878 2009/03 [Refereed][Not invited]
   

  We study lightlike surfaces in Minkowski 3-space.
• A complete classification of parallel surfaces in three-dimensional homogeneous spaces

  Jun-ichi Inoguchi, Joeri Van der Veken

  GEOMETRIAE DEDICATA 131 (1) 159 - 172 0046-5755 2008/02 [Refereed][Not invited]
   

  We complete the classification of surfaces with parallel second fundamental form in all three-dimensional homogeneous spaces.
• A Weierstrass type representation for minimal surfaces in Sol

  Jun-Ichi Inoguchi, Sungwook Lee

  PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 136 (6) 2209 - 2216 0002-9939 2008 [Refereed][Not invited]
   

  The normal Gauss map of a minimal surface in the model space Sol of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.
• 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 Belgian Mathematical Society 14 (2) 321 - 332 2007/06 [Refereed][Not invited]
   

  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.
• Biminimal submanifolds in contact 3-manifolds

  Jun-ichi Inoguchi

  BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS 12 (1) 56 - 67 1224-2780 2007 [Refereed][Not invited]
   

  We study biminimal submanifolds in contact 3-manifolds. In particular, biminimal curves in homogeneous contact Riemannian 3-manifolds and biminimal Hopf cylinders in Sasakian 3-space forms are investigated.
• 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 0004-9727 2006/12 [Refereed][Not invited]
   

  A classical theorem by Lancret says that a curve in Euclidean 3-space is of constant slope if and only if its ratio of curvature and torsion is constant. In this paper we study Lancret type problems for curves in Sasakian 3-manifolds.
• Characterizations of Bianchi-Backlund transformations of constant mean curvature surfaces

  S Kobayashi, J Inoguchi

  INTERNATIONAL JOURNAL OF MATHEMATICS 16 (2) 101 - 110 0129-167X 2005/02 [Refereed][Not invited]
   

  We show that Bianchi-Backlund transformation of a constant mean curvature surface is equivalent to the Darboux transformation and the simple type dressing.
• Timelike minimal surfaces via loop groups

  J. Inoguchi, M. Toda

  Acta Applicandae Mathematicae 83 (3) 313 - 355 0167-8019 2004/09 [Refereed]
  
• Schrodinger flows, binormal motion for curves and the second AKNS-hierarchies

  Q Ding, J Inoguchi

  CHAOS SOLITONS & FRACTALS 21 (3) 669 - 677 0960-0779 2004/07 [Refereed][Not invited]
   

  In this paper, we present a unified geometric interpretation of the second AKNS-hierarchies via the geometric concept of Schrodinger flows in the category of symplectic manifolds and binormal motion for curves in the Minkowski 3-space. (C) 2004 Elsevier Ltd. All rights reserved.
• 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 [Refereed]
  
• Minimal surfaces in 3-dimensional solvable Lie groups

  J Inoguchi

  CHINESE ANNALS OF MATHEMATICS SERIES B 24 (1) 73 - 84 0252-9599 2003/01 [Refereed][Not invited]
   

  The author studies minimal surfaces in 3-dimensional solvable Lie, groups with left invariant Riemannian metrics. A Weierstrass type integral representation formula for minimal surfaces is obtained.
• Timelike Bonnet surfaces in Lorentzian space forms

  A Fujioka, J Inoguchi

  DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 18 (1) 103 - 111 0926-2245 2003/01 [Refereed][Not invited]
   

  We study timelike surfaces in Lorentzian space forms which admit a one-parameter family of isometric deformations preserving the mean curvature. (C) 2002 Elsevier Science B.V. All rights reserved.
• 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 0393-0440 2002/04
• 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 2002 [Refereed]
  
• Darboux transformations on timelike constant mean curvature surfaces

  J Inoguchi

  JOURNAL OF GEOMETRY AND PHYSICS 32 (1) 57 - 78 0393-0440 1999/11 [Refereed][Not invited]
   

  We give loop group theoretic reformulated Backlund transformations on constant mean curvature timelike surfaces in Minkowski 3-space. Further we present 1-soliton surfaces explicitly. (C) 1999 Elsevier Science B.V. All rights reserved.
• On some generalisations of constant mean curvature surfaces

  Atsushi Fujioka, Jun-ichi Inoguchi

  Lobachevskii Journal of Mathematics 3 73 - 95 1999
• Timelike surfaces of constant mean curvature in Minkowski 3-space

  Jun-ichi INOGUCHI

  Tokyo Journal of Mathematics 21 (1) 0387-3870 1998/06/01 [Refereed]
  
• Bonnet surfaces with constant curvature

  Atsushi Fujioka, Jun-ichi Inoguchi

  Results in Mathematics 33 (3-4) 288 - 293 0378-6218 1998/05 [Refereed]
  

Books etc

• 1+3 dimensional world: From Surfcaes to Manifolds and Spacetimes

  Inoguchi, Jun-ichi (Single work)
  Gendai Sugakusha 2023/04 (ISBN: 9784768706046) 268
• Contact Geometry of Slant Submanifolds

  Inoguchi, Jun-ichi, Munteanu, Marian Ioan (ContributorSlant Curves and Magnetic Curves)
  Springer Nature Singapore Pte Ltd. 2022/06 (ISBN: 9789811600166) 

  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.
• 1+2 dimensional world: Curves and Surfaces in Minkowski Space

  Inoguchi, Jun-ichi (Single work)
  Gendai Sugakusha 2022/02 (ISBN: 9784768705766) 204
• 1+1 dimensional world: Geometry of Minkowski Plane

  Inoguchi, Jun-ichi (Single work)
  現代数学社 2021/12 189
• A First Course to Vector Analysis

  Inoguchi, Jun-ichi (Single work)
  現代数学社 2020/12 (ISBN: 9784768705476) 396
• A First Course to Partial differentiation

  Inoguchi, Jun-ichi (Single work)
  現代数学社 2019/09 (ISBN: 9784768705162) 222
• 解析学百科II 可積分系の数理

  Inoguchi, Jun-ichi (Contributor幾何学と可積分系)
  朝倉書店 2018/03
• A First Course to Lie Algebras

  Inoguchi, Jun-ichi (Single work)
  現代数学社 2018/02 (ISBN: 9784768704714) 280
• A First Course to Lie Groups

  Inoguchi, Jun-ichi (Single work)
  現代数学社 2017/07 (ISBN: 9784768704707) 272
• Surface Geometry and Integrable Systems

  Inoguchi,Jun-ichi (Single work)
  Asakura Shoten 2015/10 (ISBN: 9784254117684) vi, 212p
• 応用数理ハンドブック

  Inoguchi, Jun-ichi (Contributor幾何学と可積分系)
  朝倉書店 2013/11
• 負定曲率曲面とサイン・ゴルドン方程式

  Inoguchi, Jun-ichi (Single work)
  Saitama University 2012/04
• 離散可積分系・離散微分幾何チュートリアル2012

  Inoguchi, Jun-ichi (Contributor可積分幾何入門)
  Kyushu University 2012/03
• リッカチのひ・み・つ

  Inoguchi, Jun-ichi (Single work)
  日本評論社 2010/09
• どこにでも居る幾何. アサガオから宇宙まで

  Inoguchi, Jun-ichi (Single work)
  日本評論社 2010/09 (ISBN: 9784535786110)
• Plane curves and Solitons

  Inoguchi, Jun-ichi (Single work)
  朝倉書店 2010/03 (ISBN: 9784254117349)
• いろいろな幾何と曲線の時間発展

  Inoguchi, Jun-ichi (Single work)
  Hokkaido University 2008/09
• 幾何学いろいろ

  Inoguchi, Jun-ichi (Single work)
  日本評論社 2007/11 (ISBN: 9784535784628)
• 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 (Contributor負定曲率曲面とサイン・ゴルドン方程式)
  立教大学 2005/10

Conference Activities & Talks

• Differential Geometry of Industrial Shape Design  [Invited]

  Jun-ichi Inoguchi

  第22回水戸幾何セミナー  2023/11
• Contact geometry and magnetic trajectories  [Invited]

  Jun-ichi Inoguchi

  横国大幾何トポロジーセミナー  2023/10
• Discrete Differential Geometry. Developments and Perspectives  [Invited]

  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  2023/09
• Submanifold Geometry of LCK surfaces  [Invited]

  Jun-ichi Inoguchi

  The 20th Mito Geometry Seminar  2023/02
• Lie sphere geometry: Is it future promising?  [Invited]

  Jun-ichi Inoguchi

  Mini-Workshop "Differential Geometry, Integrable Systems, and Shape Generation"  2023/02
• アフィン接続と接触構造に関する話題から  [Invited]

  井ノ口, 順一

  福岡大学 微分幾何研究会  2021/11  福岡大学（ハイブリッド）
• Similarity geometry revisited: Differential geometry and CAGD  [Invited]

  井ノ口, 順一

  8th European Congress of Mathematics (8ECM) Minisymposium Differential Geometry: Old and New  2021/06  スロベニア Portoroz  European Mathematical Society
  
• 「離散微分幾何と有限要素法の融合，建築とCGへの応用」  [Not invited]

  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」  2020/12  九州大学（ハイブリッド）  筑波大学数理科学研究コア
  
• 3次元球面内の曲線に関する話題  [Invited]

  井ノ口, 順一

  北川義久教授ご退職記念研究集会  2020/11  東京工業大学（オンライン）
• Tzitzeica方程式をめぐって  [Invited]

  井ノ口, 順一

  リーマン面に関連する 位相幾何学  2020/08  東京大学（オンライン）
• Slant Curves in contact geometry  [Invited]

  井ノ口, 順一

  International Workshop on Geometry of Submanifolds, 2019  2019/11  トルコ Istanbul center for mathematical Science
• 3次元等質空間内の曲面のグラスマン幾何  [Invited]

  井ノ口, 順一

  北九州幾何学研究集会2019  2019/07  九州工業大学
• Harmonic map into Lie groups, revisited  [Invited]

  井ノ口, 順一

  The Joint International Meeting of the Chinese mathematical Society and American Mathematical Society  2018/06  中華人民共和国 復旦大学
• Curve flows, integrable systems and industrial design  [Invited]

  井ノ口, 順一

  Integrable Geometry at Bayrischzell  2018/05  ドイツ Bayrischzell Gasthof zur Post
• 対数型美的曲線の相似幾何学的定式化  [Invited]

  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  2018/03  中央大学  公益社団法人 精密工学会
  
• Elasticae in similarity geometry and their discretization.  [Not invited]

  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  2017/11  九州大学応用力学研究所
• Grassmann geometry of surfaces in 3-dimensional homogeneous spaces  [Invited]

  井ノ口, 順一

  INTERNATIONAL CONFERENCE ON APPLIED AND PURE MATHEMATICS (ICAPM 2017)  2017/11  ルーマニア "Gheorghe Asachi" Technical University, Iaşi
• 相似幾何不変量による平面曲線 の Fairness 測度  [Not invited]

  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  2017/09  武蔵野大学
• 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  [Not invited]

  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  2017/09  武蔵野大学
• 平面曲線と意匠設計  [Invited]

  井ノ口, 順一

  第63回幾何学シンポジウム  2016/08  岡山大学
• Grasmann geometry of 3-dimensional homogeneous spaces  [Invited]

  井ノ口,順一

  内藤博夫先生退職記念研究集会  2016/03  山口大学
• 魅力的な曲線たち  [Invited]

  井ノ口,順一

  日本数学会北海道支部会  2015/12  北海道大学  日本数学会北海道支部会
  
• Attractive plane curves in Differential Geometry  [Invited]

  Inoguchi,Jun-ichi

  Mathematical Progress in Expressive Image Synthesis 2015  2015/09  日本 九州大学  九州大学
  
• New examples of biharmonic hypersurfaces  [Not invited]

  井ノ口,順一

  International Workshop on Finite Type Submanifolds, 2014  2014/09  トルコ イスタンブール工科大学

MISC

• 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  2022/12
• ベクトル解析から曲面論へ (特集 ベクトル解析の力 : 多彩な問題を通じてその姿に迫る)

  井ノ口 順一  数理科学  52-  (8)  15  -20  2014/08
• 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  2014/06  

  "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.
• Submanifold geometry of contact 3-manifolds (Development in Differential Geometry of Submanifolds)

  Inoguchi Jun-ichi  RIMS Kokyuroku  1880-  72  -99  2014/04
• 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  2012/04
• 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  2010/02/15  

  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
• On Homogeneous Contact 3-Manifolds

  Inoguchi Jun-ichi  Bulletin of the Faculty of Education, Utsunomiya University  59-  1  -12  2009/03/10
• 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
• 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  2005/04
• Real hypersurfaces of complex space forms with symmetric Ricci *-tensor

  Hamada Tatsuyoshi, Inoguchi Jun-ichi  Memoirs of the Faculty of Science and Engineering, Shimane University. Series B, Mathematical science  38-  1–5  2005/03
• 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  2004/11
• A QUICK INTRODUCTION TO DISCRETISED PROJECTIVE DIFFERENTIAL GEOMETRY (Development in Discrete Integrable Systems : Ultra-Discretization, Quantization)

  Inoguchi Jun-ichi  RIMS Kokyuroku  1221-  112  -124  2001/07
• INTEGRABLE SURFACES AND THEIR DISCRETISATION (Recent Topics on Discrete Integrable Systems)

  Inoguchi Jun-Ichi  RIMS Kokyuroku  1170-  9  -22  2000/09
• Bonnet Surfaces with Constant Curvature (Homogeneous Structures and Theory of Submanifolds)

  Fujioka Atsushi, Inoguchi Jun-ichi  RIMS Kokyuroku  1069-  73  -82  1998/11
• SURFACES IN MINKOWSI 3-SPACE AND HARMONIC MAPS

  INOGUCHI JUN-ICHI  RIMS Kokyuroku  995-  58  -69  1997/05

Research Grants & Projects

• 双曲空間への調和写像の構成と等質空間内の曲面論への応用

  日本学術振興会：科学研究費 基盤研究(C)

  Date (from‐to) : 2019/04 -2023/03 

  Author : 井ノ口順一
• ループ群による非コンパクト対称空間への調和写像の構成と曲面論への応用

  日本学術振興会：科学研究費 基盤研究(C)

  Date (from‐to) : 2015/04 -2019/03 

  Author : 井ノ口順一
• 等質空間内の曲面のスピン幾何とループ群による構成

  日本学術振興会：科学研究費 基盤研究(C)

  Date (from‐to) : 2012/04 -2015/03 

  Author : 井ノ口順一

   

  ３次元球面内のガウス曲率が１未満の曲面に対し、ガウス曲率が一定であることが法ガウス写像の調和性で特徴づけられることを証明した。ガウス曲率が一定で１未満（ただし0でない）の曲面のループ群論的構成法を与えた。とくにガウス曲率が負の曲面と正で１未満の曲面を同時に構成することに成功した。また３次元双曲空間内のガウス曲率が一定で－１より大きく0未満の曲面に対してもループ群論的構成法を与えた。 スピン幾何とループ群論を組み合わせることにより、３次元ハイゼンベルグ群の極小曲面に対するループ群論的構成法を確立することに成功した。この構成法を用いて新しい極小曲面の例を与えた。
• Global construction of constant mean curvature surfaces in terms of contact geometry and loop groups

  日本学術振興会：科学研究費 基盤研究(C)

  Date (from‐to) : 2009/04 -2012/03 

  Author : 井ノ口順一

   

  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.
• Research on constructions of constant mean curvature surfaces in terms of conformal geometry and loop groups

  日本学術振興会：Grant-in-Aid for Scientific Research(C)

  Date (from‐to) : 2006/04 -2009/03 

  Author : 井ノ口順一

   

  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。
• 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

  日本学術振興会：科学研究費 若手研究(B)

  Date (from‐to) : 2004/04 -2006/03 

  Author : 井ノ口順一

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