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

• Project/Area Number: 18540068
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Utsunomiya University
• Principal Investigator: INOGUCHI Jun-ichi Utsunomiya University, 教育学部, 准教授 (40309886)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,700,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥600,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 平均曲率一定曲面 / 共形幾何学 / ループ群 / 調和写像 / 接触構造 / 単位接ベクトル束 / 光的曲面 / ワイエルシュトラウス公式 / 極小曲面 / 第二基本形式平行曲面 / ワイエルシュトラウス表現公式

Research Abstract

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。

Research Products

• [Journal Article] Affine biharmonic submanifolds in 3-dimensional pseudo-Hermitian geometry (2009)
  • Author(s): J.T.Cho, J.Inoguchi and J.-E.Lee
  • Journal Title: Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 79(No.1) Pages: 113-133
  • Peer Reviewed
• [Journal Article] Lightlike surfaces in Minkowski 3-space (2009)
  • Author(s): J.Inoguchi and S.Lee
  • Journal Title: International Journal of Geometric Methods on Modern Physics 6(No.2) Pages: 267-283
  • Peer Reviewed
• [Journal Article] A complete classification of parallel surfaces in three-dimensional homogeneous spaces (2009)
  • Author(s): J.Inoguchi and J.Van der Veken
  • Journal Title: Geometriae Dedicata 131 Pages: 159-172
  • Peer Reviewed
• [Journal Article] Lightlike surfaces in Minkowski 3-space (2009)
  • Author(s): J. Inoguchi and S. Lee
  • Journal Title: International Journal of Geometric Methods in Modern Physics 6 (no.21) Pages: 267-283
  • Peer Reviewed
• [Journal Article] Grassmann geometry of 3-dimensional unimodular Lie Groups I (2009)
  • Author(s): J. Inoguchi and H. Naitoh
  • Journal Title: Hokkaido Mathematical Journal (掲載決定)
  • Peer Reviewed
• [Journal Article] Parabolic geodesics in Sasakian 3-manifolds (2009)
  • Author(s): J.T. Cho, J. Inoguchi and J.-E. Lee
  • Journal Title: Canadian Mathematics Bulletin (掲載決定)
  • Peer Reviewed
• [Journal Article] Biharmonic submanifolds in 3-dimensional pseudo-Hermitian geometry (2009)
  • Author(s): J.T. Cho, J. Inoguchi and J.-E. Lee
  • Journal Title: Abhandlungen aus dem Mathematischen Seminar der Universita"t Hamburg (掲載決定)
  • Peer Reviewed
• [Journal Article] Biharmonic maps and bi-Yang-Mills fields (2009)
  • Author(s): T. Ichiyama, J. Inoguchi and H. Urakawa
  • Journal Title: Note di Matematica (掲載決定)
  • Peer Reviewed
• [Journal Article] Minimal surfaces in the 3-dimensional Heisenberg group (2008)
  • Author(s): J.Inoguchi
  • Journal Title: Differential-Geometry Dynamical Systems 10 Pages: 163-169
  • Peer Reviewed
• [Journal Article] 戸田方程式と微分幾何 (2008)
  • Author(s): 井ノ口順一
  • Journal Title: 九州大学応用力学研究所講究録19ME-S2 Article Number 9
• [Journal Article] A Weierstrass representation for minimal surfaces in Sol (2008)
  • Author(s): J.Inoguchi and S.Lee
  • Journal Title: Proceedings of American Mathematical Society 136 Pages: 2209-2216
  • Peer Reviewed
• [Journal Article] A complete classification of parallel surfaces in three-dimensional homogeneous spaces (2008)
  • Author(s): J. Inoguchi and J. Van der Veken
  • Journal Title: Geometriae Dedicata 131 Pages: 159-172
  • Peer Reviewed
• [Journal Article] Minimal surfaces in the 3-dimensional Heisenberg group (2008)
  • Author(s): J. Inoguchi
  • Journal Title: Differential Geometry-Dynamical Systems 10 Pages: 163-169
  • Peer Reviewed
• [Journal Article] 戸田方程式と微分幾何 (2008)
  • Author(s): 井ノ口順一
  • Journal Title: 九州大学応用力学研究所講究録 19ME-S2
• [Journal Article] 黒微分とDS方程式のはなし (2007)
  • Author(s): 井ノ口順一
  • Journal Title: 九州大学応用力学研究所講究録18ME-S5 Article Number 15
• [Journal Article] Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces (2007)
  • Author(s): F.Bekkar, F.Bouziani, Y.Boukhatem and J.Inoguchi
  • Journal Title: Differntial Geometry -Dynamical Systems 9 Pages: 21-39
  • Peer Reviewed
• [Journal Article] Parallel surfaces in the motion groups E(1, 1) and E(2) (2007)
  • Author(s): J.Inoguchi and J.Van der Veken
  • Journal Title: Bulletin of the Belgian Mathematical Society Simon Stevin 14 Pages: 317-320
  • Peer Reviewed
• [Journal Article] A Weierstrass representation for minimal surfaces in Sol (2007)
  • Author(s): J.Inoguchi, S.Lee
  • Journal Title: Proceedings of American Mathematical Society (印刷中)
• [Journal Article] Parallel surfaces in the motion groups in E(1,1) and E(2) (2007)
  • Author(s): J.Inoguchi, J.Van der Veken
  • Journal Title: Bulletin of the Belgian Mathematical Society 14-2 Pages: 321-322
• [Journal Article] Helicoids and Axially symmetric minimal surfaces in 3-dimensional homogeneous spaces (2007)
  • Author(s): F.Bekkar, F.Bouziani, Y.Boukhatem, J.Inoguchi
  • Journal Title: Differential Geometry - Dymanical Systems 9 Pages: 21-39
• [Journal Article] 黒微分とDS方程式のはなし (2007)
  • Author(s): 井ノ口順一
  • Journal Title: 九州大学応用力学研究所研究報告 18
• [Journal Article] Biharmonic maps and bi-Yang-Mills fields
  • Author(s): T.Ichiyama, J.Inoguchi and H.Urakawa
  • Journal Title: Note di Matematica (印刷中)
  • Peer Reviewed
• [Journal Article] Grassmann geometry of 3-dimensional unimodular Lie groups I
  • Author(s): J. Inoguchi and H.Naitoh
  • Journal Title: Hokkaido Mathematical Journal (印刷中)
  • Peer Reviewed
• [Journal Article] Parabolic geodesics in Sasakian 3-manifolds
  • Author(s): J.T.Cho, J.Inoguchi and J.-E.Lee
  • Journal Title: Canadian MatematicsBulletin (印刷中)
  • Peer Reviewed
• [Presentation] 戸田格子の微分幾何 (2007)
  • Author(s): 井ノ口順一
  • Organizer: 研究集会「戸田格子40周年. 非線形波動研究の歩みと展望」
  • Place of Presentation: 九州大学応用力学研究所
  • Year and Date: 2007-11-08
• [Presentation] Affine spheres of finite type (2007)
  • Author(s): 井ノ口順一
  • Organizer: DMHF2007 COE conference on the development of Dynamic Mathematics with high functionality
  • Place of Presentation: 福岡リーセントホテル
  • Year and Date: 2007-10-02
• [Presentation] Biharmonic maps and bi-Yang Mills fields (2007)
  • Author(s): 一山稔之・井ノ口順一・浦川肇
  • Organizer: 日本数学会秋季総合分科会(幾何学分科会)
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-21
• [Presentation] 黒微分とDS方程式のはなし (2006)
  • Author(s): 井ノ口順一
  • Organizer: 研究集会「非線形波動現象における基礎理論,数値計算および実験のクロスオーバー」
  • Place of Presentation: 九州大学応用力学研究所
  • Year and Date: 2006-11-18
• [Presentation] Classification of surfaces with parallel second fundamental form in 3-dimensional homogeneous spaces (2006)
  • Author(s): Jun-ichi Inoguchi
  • Organizer: London Mathematical Society Durham Conference, Methods of Integrable Sytems in Geometry (informal seminar)
  • Place of Presentation: ダーラム大学(Durham University, 英国)
  • Year and Date: 2006-08-24
• [Book] いろいろな幾何と曲線の時間発展,(北海道大学数学講究録138)(幾何学いろいろ) (2008)
  • Author(s): 井ノ口順一
  • Total Pages: 66
  • Publisher: (北海道大学理学部数学教室)日本評論社
• [Book] 幾何学いろいろ (2007)
  • Author(s): 井ノ口順一
  • Total Pages: 209
  • Publisher: 日本評論社