Researcher basic information

• 博士 （理学）, 神戸大学

• https://researchmap.jp/shimpeister?lang=en

• https://jglobal.jst.go.jp/detail?JGLOBAL_ID=200901083779087841
• https://sites.google.com/site/kobayashishimpeisite/

• 200901083779087841

• 幾何学
• 微分幾何
• ループ群
• 可積分系
• 線型常微分方程式
• 平均曲率一定曲面
• 可視化
• コンピュータ実験
• Discretization

• Natural Science, Geometry, 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

• The Evolution of a Curve Induced by the Pohlmeyer-Lund-Regge Equation.
  Shimpei Kobayashi; Yuhei Kogo; Nozomu Matsuura
  Journal of Nonlinear Science, 35, 4, 85, 85, Aug. 2025, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal
• Maximal surfaces in the Lorentzian Heisenberg group
  DAVID BRANDER; SHIMPEI KOBAYASHI
  Mathematical Proceedings of the Cambridge Philosophical Society, 1, 30, Cambridge University Press (CUP), 29 Jul. 2025, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal, Abstract
  
  The 3-dimensional Heisenberg group can be equipped with three different types of left-invariant Lorentzian metric, according to whether the center of the Lie algebra is spacelike, timelike or null. Using the second of these types, we study spacelike surfaces of mean curvature zero. These surfaces with singularities are associated with harmonic maps into the 2-sphere. We show that the generic singularities are cuspidal edge, swallowtail and cuspidal cross-cap. We also give the loop group construction for these surfaces, and the criteria on the loop group potentials for the different generic singularities. Lastly, we solve the Cauchy problem for harmonic maps into the 2-sphere using loop groups, and use this to give a geometric characterisation of the singularities. We use these results to prove that a regular spacelike maximal disc with null boundary must have at least two cuspidal cross-cap singularities on the boundary.
• A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions
  Shimpei Kobayashi; Yu Ohno
  Osaka Journal of Mathematics, 62, 2, 329, 349, 01 Apr. 2025, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal, We study a statistical manifold $(\mathcal{N}, g^F, \nabla^{A}, \nabla^{A*})$
  of multivariate normal distributions, where $g^F$ is the Fisher metric and
  $\nabla^{A}$ is the Amari-Chentsov connection and $\nabla^{A*}$ is its
  conjugate connection. We will show that it admits a solvable Lie group
  structure and moreover the Amari-Chentsov connection $\nabla^{A}$ on
  $(\mathcal{N}, g^F)$ will be characterized by the conjugate symmetry, i.e., a
  curvatures identity $R=R^*$ of a connection $\nabla$ and its conjugate
  connection $\nabla^*$.
• The Complex Landslide Flow and the Method of Integrable Systems
  Shimpei Kobayashi
  International Mathematics Research Notices, 2025, 7, Oxford University Press (OUP), 24 Mar. 2025, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal, Abstract
  
  We investigate a connection between the complex landslide flow, defined on a pair of Teichmüller spaces, and the integrable system approach to harmonic maps into a symmetric space. We will prove that the holonomy of the complex landslide flow can be derived from the holonomy of the family of flat connections determined by a harmonic map into the hyperbolic two-space.
• Half-Dimensional Immersions into the Para-Complex Projective Space and Ruh–Vilms Type Theorems
  Josef F. Dorfmeister; Roland Hildebrand; Shimpei Kobayashi
  Results in Mathematics, 79, 7, Springer Science and Business Media LLC, 09 Sep. 2024, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal
• A classification of constant Gaussian curvature surfaces in the three-dimensional hyperbolic space
  Junichi Inoguchi; Shimpei Kobayashi
  12 Apr. 2024
  Weakly complete constant Gaussian curvature $-1classified in terms of holomorphic quadratic differentials. For this purpose,
  we will first establish a loop group method for constant Gaussian curvature
  surfaces in $\mathbb H^3$ with $K>-1$ but $K \neq 0$ by using harmonicities of
  Lagrangian and Legendrian Gauss maps. Then we will show that a spectral
  parameter deformation of the Lagrangian harmonic Gauss map gives a harmonic map
  into $\mathbb H^2$ for $-1< K<0$ or $\mathbb S^2$ for $K>0$, respectively.
• Geodesics of multivariate normal distributions and a Toda lattice type Lax pair
  Shimpei Kobayashi
  Physica Scripta, 98, 11, 115241, 115241, IOP Publishing, 17 Oct. 2023, [Peer-reviewed], [International Magazine]
  Scientific journal, Abstract
  
  We study geodesics of multivariate normal distributions with respect to the Fisher metric. First it will be shown that a computational formula for geodesics can be understood using the block Cholesky decomposition and a natural Riemannian submersion. Next a mid point algorithm for geodesics will be obtained. And finally a new Toda lattice type Lax pair will be derived from the geodesic and the block Cholesky decomposition.
• Minimal cylinders in the three-dimensional Heisenberg group
  Shimpei Kobayashi
  Mathematische Annalen, 388, 3, 3299, 3317, Springer Science and Business Media LLC, 24 Mar. 2023, [Peer-reviewed], [International Magazine]
  Scientific journal
• Discrete constant mean curvature surfaces on general graphs
  Tim Hoffmann; Shimpei Kobayashi; Zi Ye
  Geometriae Dedicata, 216, 6, Springer Science and Business Media LLC, Dec. 2022, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  English, Scientific journal, Abstract
  
  The contribution of this paper is twofold. First, we generalize the definition of discrete isothermic surfaces. Compared with the previous ones, it covers more discrete surfaces, e.g., the associated families of discrete isothermic minimal and non-zero constant mean curvature (CMC in short) surfaces, whose counterpart in smooth case are isothermic surfaces. Second, we show that the discrete isothermic CMC surfaces can be obtained by the discrete holomorphic data (a solution of the additive rational Toda system) via the discrete generalized Weierstrass type representation., 30360916
• 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], ［Internationally co-authored］, [International Magazine]
  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.
• Timelike Minimal Surfaces in the Three-Dimensional Heisenberg Group
  Hirotaka Kiyohara; Shimpei Kobayashi
  The Journal of Geometric Analysis, 32, 8, Springer Science and Business Media LLC, Aug. 2022, [Peer-reviewed], [International Magazine]
  Scientific journal
• On a constant curvature statistical manifold
  Shimpei Kobayashi; Yu Ohno
  Information Geometry, Springer Science and Business Media LLC, 15 Feb. 2022, [Peer-reviewed], [International Magazine]
  Scientific journal
• A characterization of the alpha-connections on the statistical manifold of normal distributions
  Hitoshi Furuhata; Jun-ichi Inoguchi; Shimpei Kobayashi
  Information Geometry, 4, 1, 177, 188, Springer Science and Business Media LLC, Jul. 2021, [Peer-reviewed], [International Magazine]
  We study a statistical manifold $(\mathcal{N}, g^F, \nabla^{A}, \nabla^{A*})$
  of multivariate normal distributions, where $g^F$ is the Fisher metric and
  $\nabla^{A}$ is the Amari-Chentsov connection and $\nabla^{A*}$ is its
  conjugate connection. We will show that it admits a solvable Lie group
  structure and moreover the Amari-Chentsov connection $\nabla^{A}$ on
  $(\mathcal{N}, g^F)$ will be characterized by the conjugate symmetry, i.e., a
  curvatures identity $R=R^*$ of a connection $\nabla$ and its conjugate
  connection $\nabla^*$.
• Ruh–Vilms theorems for minimal surfaces without complex points and minimal Lagrangian surfaces in $$\mathbb {C}P^2$$
  Josef F. Dorfmeister; Shimpei Kobayashi; Hui Ma
  Mathematische Zeitschrift, 296, 3-4, 1751, 1775, Springer Science and Business Media LLC, Dec. 2020, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal
• The Gauss maps of Demoulin surfaces with conformal coordinates
  Jun-ichi Inoguchi; Shimpei Kobayashi
  Science China Mathematics, 64, 7, 1479, 1492, Springer Science and Business Media LLC, 21 Sep. 2020, [Peer-reviewed], [International Magazine]
  Scientific journal
• Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space
  Josef F. Dorfmeister; Shimpei Kobayashi
  Annali di Matematica Pura ed Applicata (1923 -), 200, 2, 521, 546, Springer Science and Business Media LLC, 05 Jun. 2020, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  English, Scientific journal
• Representation formula for discrete indefinite affine spheres
  Shimpei Kobayashi; Nozomu Matsuura
  Differential Geometry and its Applications, 69, 101592, 101592, Elsevier BV, Apr. 2020, [Peer-reviewed], [International Magazine]
  Scientific journal
• Survey on real forms of the complex A2(2)-Toda equation and surface theory
  Josef F. Dorfmeister; Walter Freyn; Shimpei Kobayashi; Erxiao Wang
  Complex Manifolds, 6, 1, 194, 227, Walter de Gruyter GmbH, 01 Jan. 2019, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  Scientific journal, The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups [9] states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop parameter. As a matter of fact, the same result holds for k-symmetric spaces over reductive Lie groups, [8].
  
  In this survey we will show that to each of the five different types of real forms for a loop group of A₂⁽²⁾ there exists a surface class, for which some frame is integrable for all values of the loop parameter if and only if it belongs to one of the surface classes, that is, minimal Lagrangian surfaces in ℂℙ², minimal Lagrangian surfaces in ℂℍ², timelike minimal Lagrangian surfaces in ℂℍ₁², proper definite affine spheres in ℝ³ and proper indefinite affine spheres in ℝ³, respectively.
• Nonlinear d'Alembert formula for discrete pseudospherical surfaces
  Shimpei Kobayashi
  JOURNAL OF GEOMETRY AND PHYSICS, 119, 208, 223, Sep. 2017, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• A loop group method for affine harmonic maps into Lie groups
  Josef F. Dorfmeister; Jun-ichi Inoguchi; Shimpei Kobayashi
  Advances in Mathematics, 298, 207, 253, Aug. 2016, [Peer-reviewed]
  Scientific journal
• A construction method for discrete constant negative Gaussian curvature surfaces
  Shimpei Kobayashi
  Mathematical Progress in Expressive Image Synthesis III, Extended and Selected Results from the Symposium MEIS2015, 21, 33, Apr. 2016, [International Magazine]
  Scientific journal, This article is an application of the author's paper about a construction
  
  method for discrete constant negative Gaussian curvature surfaces, the
  
  nonlinear d'Alembert formula. The heart of this formula is the Birkhoff
  
  decomposition, and we give a simple algorithm for the Birkhoff decomposition.
  
  As an application, we draw figures of discrete constant negative Gaussian
  
  curvature surfaces given by this method.
• 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]
  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
• A loop group method for Demoulin surfaces in the 3-dimensional real projective space
  Shimpei Kobayashi
  Differential Geometry and its Applications, 40, 57, 66, Jun. 2015, [Peer-reviewed]
  Scientific journal
• 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
• Constant mean curvature surfaces in hyperbolic 3-space via loop groups
  Josef F. Dorfmeister; Jun-ichi Inoguchi; Shimpei Kobayashi
  Journal für die reine und angewandte Mathematik (Crelles Journal), 2014, 686, 1, 36, 01 Jan. 2014, [Peer-reviewed]
  Scientific journal
• Discretization of integrable systems via dressing actions.
  KOBAYASHI Shimpei
  RIMS Kôkyûroku Bessatsu, B41, 161, 171, Kyoto University, 2013, [Peer-reviewed], [Domestic magazines]
• Real forms of complex surfaces of constant mean curvature
  Shimpei Kobayashi
  Transactions of the American Mathematical Society, 363, 04, 1765, 1765, American Mathematical Society (AMS), 01 Apr. 2011, [Peer-reviewed], [International Magazine]
  Scientific journal
• TOTALLY SYMMETRIC SURFACES OF CONSTANT MEAN CURVATURE IN HYPERBOLIC 3-SPACE
  SHIMPEI KOBAYASHI
  Bulletin of the Australian Mathematical Society, 82, 2, 240, 253, 18 Jun. 2010
  Scientific journal
• Complex surfaces of constant mean curvature fibered by minimal surfaces
  Josef Dorfmeister; Shimpei Kobayashi; Franz Pedit
  Hokkaido Mathematical Journal, 39, 1, 1, 55, Feb. 2010, [Peer-reviewed], ［Internationally co-authored］, [International Magazine]
  English, Scientific journal
• Note on equivariant harmonic maps in complex projective spaces
  Shimpei Kobayashi
  Annals of Global Analysis and Geometry, 36, 4, 375, 380, 10 May 2009, [Peer-reviewed]
  Scientific journal
• Asymptotics of ends of constant mean curvature surfaces with bubbletons
  Shimpei Kobayashi
  PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136, 4, 1433, 1443, 2008, [Peer-reviewed]
  English, Scientific journal
• Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms
  N. Schmitt; M. Kilian; S.-P. Kobayashi; W. Rossman
  JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 75, 563, 581, Jun. 2007, [Peer-reviewed]
  English, Scientific journal
• Coarse classification of constant mean curvature cylinders
  J. Dorfmeister; S.-P. Kobayashi
  Transactions of the American Mathematical Society, 359, 6, 2483, 2500, 04 Jan. 2007
  Scientific journal
• CONSTANT MEAN CURVATURE SURFACES OF ANY POSITIVE GENUS
  M. KILIAN; S.-P. KOBAYASHI; W. ROSSMAN; N. SCHMITT
  Journal of the London Mathematical Society, 72, 01, 258, 272, 20 Jul. 2005
  Scientific journal
• CHARACTERIZATIONS OF BIANCHI–BÄCKLUND TRANSFORMATIONS OF CONSTANT MEAN CURVATURE SURFACES
  SHIMPEI KOBAYASHI; JUN-ICHI INOGUCHI
  International Journal of Mathematics, 16, 02, 101, 110, Feb. 2005, [Peer-reviewed]
  Scientific journal
• Loop Group Methods for Constant Mean Curvature Surfaces
  Shimpei KOBAYASHI
  Rokko Lectures in Mathematics, 2005, [Domestic magazines]
  Scientific journal
• Bubbletons in 3-dimensional space forms
  KOBAYASHI Shimpei
  Balkan Journal of Geometry and its Applications, 9, 1, 44, 68, 2004, [Peer-reviewed]
  English, Scientific journal

• 曲面とベクトル解析
  小林, 真平
  日本評論社, Dec. 2016, 9784535806375, vi, 216p, Japanese
• 部分多様体の微分幾何学の深化
  京都大学数理解析研究所; 小林, 真平
  京都大学数理解析研究所, Apr. 2014, ii, 189p
• 曲面の微分幾何学とソリトン方程式 : 可積分幾何入門
  井ノ口, 順一; 小林, 真平; 松浦, 望; 立教大学
  [立教大学], Feb. 2005, ii, 117, 28, 56p, Japanese
• Loop group methods for constant mean curvature surfaces
  Fujimori, Shoichi; 小林, 真平; Rossman, Wayne
  Department of Mahtematics, Faculty of Science, Kobe University, 2005, 4907719175, v, 118 p., English

• 幾何学講義, 2024年, 修士課程, 理学院
• 幾何学特別講義, 2024年, 修士課程, 理学院
• 国際交流Ⅱ, 2024年, 学士課程, 国際本部
• 幾何学続論, 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
• 線形代数学Ⅱ, 2024年, 学士課程, 全学教育
• 数学特別講義Ⅱ, 2024年, 学士課程, 理学部

• Comprehensive study of various geometries with harmonic maps to symmetric spaces as a core
  Grants-in-Aid for Scientific Research
  01 Apr. 2022 - 31 Mar. 2027
  小林 真平
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 22K03304
• Fusion of discrete and smooth integrable geometry
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  01 Apr. 2018 - 31 Mar. 2022
  小林 真平
  本年度は，まず離散平均曲率一定曲面の一般化について，ワイエルシュトラス型の表現公式を用いて研究した（ミュンヘン工科大学のHoffmann氏とYe氏との共同研究）．ワイエルシュトラス型の表現公式に付随する複比のシステムをaddtive-rational戸田系と対応づけること及び，ループ群の分解定理を用いることにより，自然に離散平均曲率一定曲面の離散化が得られる．現在，研究結果を纏めている．
  
  
  また，A_2^(2)型のアフィン・カッツ-ムーディリー代数の実形の分類を用いて，新しい可積分曲面の類を見つけた（ミュンヘン工科大学のDorfmeister氏との共同研究）．これは，これまでに見つかっていなかった可積分曲面の類であり，アフィン・カッツ-ムーディリー代数の実形の分類が，可積分曲面の研究に非常に重要であることの証左である．その研究結果を現在纏めている．また，これに関連して，A_2^(2)型のアフィン・カッツ-ムーディリー代数の実形（5つ存在する）と可積分曲面の完全な対応に関してのサーベイ論文を執筆した（Dorfmeister氏，Freyn氏，Wang氏との共著）．
  
  
  さらに，３次元ハイゼンベルグ群の極小曲面の大域的な性質について研究した（Dorfmeister氏と筑波大学の井ノ口氏との共同研究）．極小曲面がいつ非自明な位相を持つかの特徴づけなどを得ることができ，極小回転面の構成を具体的に与えた．また，今後の研究の基礎となる部分も一緒に纏め現在投稿中である．
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 18K03265
• A Weierstrass type representation for surfaces via loop group method and its applications
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  01 Apr. 2014 - 31 Mar. 2018
  Kobayashi Shimpei
  Surfaces whose structure equation can be given by an integrable system are often called integrable surfaces. Here the integrable systems is a generic term used to refer to solvable (partial) differential equations. In particular many integrable surfaces have a Weierstrass type representation in terms of loop groups and holomorphic functions.
  In this research we studied integrable surfaces by using the Weierstrass type representation. Concretely, we studied affine harmonic maps, constant Gaussian curvature surfaces in 3-dimensional hyperbolic space, discrete affine spheres, affine plane curves and maximal surfaces in 3-dimensional Anti-de Sitter space.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 26400059
• Systematic development and application of methods in differential geometry and integrable systems motivated by quantum cohomology
  Grants-in-Aid for Scientific Research
  21 Oct. 2013 - 31 Mar. 2018
  Guest Martin; OHNITA Yoshihiro; MAEDA Yoshiaki; SERGEI V Ketov; SAKAI Takashi; OTOFUJI Takashi; AKAHO Manabu; KOBAYASHI Shimpei; IRITANI Hiroshi; HOSONO Shinobu
  A series of methods for solving the tt*-Toda equations were developed during the course of this project. These methods used p.d.e. theory, integrable systems theory, and Lie theory. Our main results were achieved for the tt*-Toda equations of type A_n. Here we give a complete treatment of the solutions and their asymptotic data and monodromy data. A more abstract approach was used in the case n=1, in order to describe the moduli space of solutions. These results were motivated in part by the special solutions corresponding to quantum cohomology rings of Kaehler manifolds. In order to promote research in this area, a number of conferences, workshops, and seminars by specialists were organised.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Waseda University, 25247005
• Exploitation of new relations between differential geometry and quantum cohomology in the context of integrable systems
  Grants-in-Aid for Scientific Research
  2009 - 2012
  GUEST Martin; KAMISHIMA Yoshinobu; TOKUNAGA Hiroo; MAEDA Yoshiaki; MIYAOKA Reiko; KOHNO Toshitake; OHNITA Yoshihiro; SAKAI Takashi; SERGEI V Ketov; AKAHO Manabu; OTOFUJI Takashi; KOBAYASHI Shinpei; KUROSU Sanae
  We have made progress with some key examples, which demonstrate interesting and nontrivial phenomena. In "Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa" (M. Guest and C.-S. Lin, J. reine angew. Math., 2012, in press) the existence of a family of smooth solutions of the tt*-Toda equation was established. This was a technical breakthrough: p.d.e. methods are well suited to the noncompact case, where standard loop group methods fail. In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (M. Guest, A. Its, and C.-S. Lin, arXiv:1209.2045), a second technical breakthrough was made, by relating the global smoothness of the solutions to the monodromy data (Stokes data) of an associated linear equation. This Stokes data was computed explicitly for all globally smooth solutions of the tt*-Toda equation. We expect that these techniques will be applicable to other problems in differential geometry.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), 21244004
• Construction of surfaces via complexifications of loop groups
  Grants-in-Aid for Scientific Research
  2011 - 2011
  KOBAYASHI Shimpei
  When the structure equations (nonlinear partial differential equations) of a surface is an integrable system, the surface is called "integrable surface". In the research, we gave constructions and characterizations of integrable surfaces. In particular, using loop group structures of integrable surfaces, we gave a construction of minimal surfaces in the three-dimensional Heisenberg group, constant Gaussian curvature surfaces in the three-sphere and a characterization of Demoulin surfaces in the three-dimensional real projective space. Moreover, we gave a new method obtaining the discrete mKdV equation using a loop group action.
  Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (B), 弘前大学, Principal investigator, Competitive research funding, 23740042
• Asymptotic behavior of surfaces with special properties via transformation theory and conserved quantities and integrable systems techniques
  Grants-in-Aid for Scientific Research
  2008 - 2011
  W.F Rossma; NORO Masayuki; KOIKE Tatsuya
  The purpose of this research was to expand our understanding of discretizations in surface theory, in a way that would preserve the geometric mathematical structure (such as the notion of isothermicity, and various transformations like the Christoffel and Calapso and Darboux and Baecklund transformations) that exists for smooth surfaces.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Kobe University, 20340012
• A construction of surfaces in spaces of constant curvature via integrable system method
  Grants-in-Aid for Scientific Research
  2008 - 2010
  KOBAYASHI Sinpei
  We defined complex constant mean curvature surfaces by a natural generalization of constant mean curvature surfaces in Euclidean three space and classified real form surfaces, such as constant mean curvature or constant Gauss curvature surfaces in spaces of constant curvature, for a complex constant mean curvature surface. We also characterized equivariant harmonic maps in complex projective spaces via potentials, which are matrix valued 1-forms. Moreover, a construction method of equivariant harmonic maps in complex projective spaces has been obtained from the potentials.
  Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (B), Hirosaki University, Principal investigator, Competitive research funding, 20740045
• Differential geometric researches on surfaces in a space of constant curvature and their singularities
  Grants-in-Aid for Scientific Research
  2006 - 2009
  KOKUBU Masatoshi; IRIE Hiroshi; KOBAYASHI Shimpei; ROSSMAN Wayne
  We studied surfaces in a three-dimensional manifold of constant negative curvature, called the hyperbolic space, requiring them to have good properties from the differential-geometric viewpoint. (Note that the hyperbolic space has interesting features beyond our common sense, e.g., a single hyperbolic line has infinitely many parallels.) We clarified the asymptotic behavior of ends of flat surfaces admitting singularities. Concerning linear Weingarten surfaces, we had a global representation formula, criterion for the shape of singularities, the orientability and co-orientability, and so on.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Tokyo Denki University, 18540096
• Research on quantum cohomology, Frobenius manifolds, and harmonic maps related to integrable systems
  Grants-in-Aid for Scientific Research
  2006 - 2008
  MARTIN Guest; SERGEI V. Ketov
  この研究は可積分系(大きな群対称性を持つ微分方程式系)に関連した現代幾何学の諸問題に関わる研究である。これらの問題は(曲面論を含む)古典的な微分幾何学および量子論と弦理論の幾何学に端を発する。
  ループ群や無限次元グラスマン多様体の理論をはじめ、無限次元の手法が用いられる。主要な結果の1つとして、D加群による量子コホモロジーの理論への新しいアプローチが挙げられる。このプロジェクトの大きな特徴は、この研究領域を発展させるために、この分野をリードする国内外の研究者達と共同で研究活動を行うことである。
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Tokyo Metropolitan University, 18204005