General study on curves and surfaces related to integrable systems

• Project/Area Number: 18540074
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Hitotsubashi University
• Principal Investigator: FUJIOKA Atsushi Hitotsubashi University, 大学院・経済学研究科, 准教授 (30293335)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,020,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥720,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 微分幾何 / 曲線 / 曲面 / 可積分系 / アファイン微分幾何 / 典線

Research Abstract

平均曲率ベクトルの大きさを保ちながら等長的に変形可能な4次元空間形内の曲面について調べ、3次元空間形内の曲面とは見なされない例を構成した。中心アファイン計量の面積積分の停留曲面として得られる中心アファイン極小曲面について新しい例をみつけた他、自己合同中心写像をもつ中心アファイン曲面についても考察した。曲率が可積分系に現れる微分方程式に従う曲線の運動のハミルトン系としての特徴付けについて調べた

Research Products

• [Journal Article] Centroaffine minimal surfaces whose centroaffine curvature and Pick function are constants (2010)
  • Author(s): Atsushi Fujioka
  • Journal Title: Journal of Mathematical Analysis and Applications 365 Pages: 694-700
  • NAID: 120006931764
  • Peer Reviewed
• [Journal Article] Hamiltonian formalism for the higher KdV flows on the space of closed complex equicentroaffine curves (2010)
  • Author(s): Atsushi Fujioka, Takashi Kurose
  • Journal Title: International Journal of Geometric Methods in Modern Physics 7 Pages: 165-175
  • Peer Reviewed
• [Journal Article] Hamiltonian formalism for the higher KdV flows on the space of closed complex equicentroaffine curves (2010)
  • Author(s): Atsushi Fujioka, Takashi Kurose
  • Journal Title: International Journal of Geometric Methods in Modern Physics Vol. 7 Pages: 165-175
  • Peer Reviewed
• [Journal Article] Centroaffine minimal surfaces whose centroaffine curvature and Pick function are constants (2010)
  • Author(s): Atsushi Fujioka
  • Journal Title: Journal of Mathematical Analysis and Applications Vol. 365 Pages: 694-700
  • NAID: 120006931764
  • Peer Reviewed
• [Journal Article] Centroaffine minimal surfaces with non-semisimple centroaffine Tchebychev operator (2009)
  • Author(s): Atsushi Fujioka
  • Journal Title: Results in Mathematics 56 Pages: 177-195
  • NAID: 120002674979
  • Peer Reviewed
• [Journal Article] Geometry of the space of closed curves in the complex hyperbola (2009)
  • Author(s): Atsushi Fujioka, Takashi Kurose
  • Journal Title: The Kyushu Journal of Mathematics 63 Pages: 161-165
  • NAID: 130000135277
  • Peer Reviewed
• [Journal Article] Geometry of the space of closed curves in the complex hyperbola (2009)
  • Author(s): Atsushi Fujioka, Takashi Kurose
  • Journal Title: The Kyushu Journal of Mathematics Vol. 63 Pages: 161-165
  • NAID: 130000135277
  • Peer Reviewed
• [Journal Article] Centroaffine minimal surfaces with non-semisimple centroaffine Tchebychev operator (2009)
  • Author(s): Atsushi Fujioka
  • Journal Title: Results in Mathematics Vol. 56 Pages: 177-195
  • NAID: 120002674979
  • Peer Reviewed
• [Journal Article] Motions of curves in the complex hyperbola and the Burgers hierarchy (2008)
  • Author(s): Atsushi Fujioka, TakashiKurose
  • Journal Title: Osaka Journal of Mathematics 45 Pages: 1057-1065
  • NAID: 120004840816
  • Peer Reviewed
• [Journal Article] Timelike surfaces with harmonic inverse mean curvature (2008)
  • Author(s): Atsushi Fujioka, Jun-ichi Inoguchi
  • Journal Title: Advanced Studies in Pure Mathematics 51 Pages: 113-141
  • Peer Reviewed
• [Journal Article] Bonnet surfaces with non-flat normal bundle in the hyperbolic four-space (2008)
  • Author(s): Atsushi Fujioka
  • Journal Title: Far East Journal of Mathematical Sciences 30 Pages: 381-387
  • NAID: 120002950425
  • Peer Reviewed
• [Journal Article] Timelike surfaces with harmonic inverse mean curvature (2008)
  • Author(s): Atsushi Fujioka and Jun-ichi Inoguchi
  • Journal Title: Advanced Studies in Pure Mathematics 51 Pages: 113-141
  • Peer Reviewed
• [Journal Article] Motions of curves in the complex hyperbola and the Burgers hierarchy (2008)
  • Author(s): Atsushi Fujioka and Takashi Kurose
  • Journal Title: Osaka Journal of Mathematics 45 Pages: 1057-1065
  • NAID: 120004840816
  • Peer Reviewed
• [Journal Article] Bonnet surfaces with non-flat normal bundle in thehyperbolic four-space (2008)
  • Author(s): Atsushi Fujioka
  • Journal Title: Far East Journal of Mathematical Sciences 30 Pages: 381-387
  • Peer Reviewed
• [Journal Article] Motions of curves in the complex hyperbola and theBurgers hierarchy (2008)
  • Author(s): Atsushi Fujioka, Takashi Kurose
  • Journal Title: Osaka Journal of Mathematics 45 Pages: 1057-1065
  • Peer Reviewed
• [Journal Article] Deformations of surfaces preserving conformal or similarity invariants (2007)
  • Author(s): Atsushi Fujioka, Jun-ichi Inoguchi
  • Journal Title: Progress in Mahtematics 252 Pages: 53-67
  • Peer Reviewed
• [Journal Article] Deformations of surfaces preserving conformal or similarity invariants (2007)
  • Author(s): Atsushi Fujioka and Jun-ichi Inoguchi
  • Journal Title: Progress in Mahtematics 252 Pages: 53-67
  • Peer Reviewed
• [Journal Article] Deformations of surfaces preserving conformal or similarity invariants (2007)
  • Author(s): A.Fujioka, J.Inoguchi
  • Journal Title: Progress in Mathematics 252 Pages: 53-67
• [Presentation] 変分問題とアファイン微分幾何 (2010)
  • Author(s): 藤岡敦
  • Organizer: 沖縄高専数学セミナー
  • Place of Presentation: 沖縄
  • Year and Date: 2010-01-29
• [Presentation] 変分問題とアファイン微分幾何 (2010)
  • Author(s): 藤岡敦
  • Organizer: 沖縄高専数学セミナー
  • Place of Presentation: 沖縄工業高等専門学校
  • Year and Date: 2010-01-29
• [Presentation] 中心アファイン極小曲面 (2009)
  • Author(s): 藤岡敦
  • Organizer: 福岡大学微分幾何研究会
  • Place of Presentation: 福岡大学
  • Year and Date: 2009-11-20
• [Presentation] Centroaffine minimal surfaces、統計多様体の幾何学とその周辺 (2009)
  • Author(s): 藤岡敦
  • Organizer: 特異点論セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2009-11-06
• [Presentation] Centroaffine minimal surfaces (2009)
  • Author(s): 藤岡敦
  • Organizer: 統計多様体の幾何学とその周辺, 特異点論セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2009-11-06
• [Presentation] 等積中心アファイン曲線とAKNS系 (2009)
  • Author(s): 藤岡敦
  • Organizer: 福岡大学応用数学教室談話会
  • Place of Presentation: 福岡大学
  • Year and Date: 2009-02-26
• [Presentation] 複素双曲線上の閉曲線のなす空間 (2008)
  • Author(s): 藤岡敦
  • Organizer: 多様体上の幾何構造とその応用
  • Place of Presentation: 名城大学
  • Year and Date: 2008-03-08
• [Presentation] 複素双曲線上の曲線のなす空間 (2008)
  • Author(s): 藤岡 敦
  • Organizer: 多様体上の幾何構造とその応用
  • Place of Presentation: 名城大学
  • Year and Date: 2008-03-08
• [Presentation] 複素双曲線上の曲線の運動 (2007)
  • Author(s): 藤岡敦
  • Organizer: 多様体上の微分方程式
  • Place of Presentation: いしかわシティカレッジ
  • Year and Date: 2007-12-10
• [Presentation] 複素双曲線上の曲線の運動と離散化 (2007)
  • Author(s): 藤岡敦
  • Organizer: 熊本大学数学談話会
  • Place of Presentation: 熊本大学
  • Year and Date: 2007-10-17
• [Presentation] 複素双曲線上の曲線の運動と離散化 (2007)
  • Author(s): 藤岡敦
  • Organizer: 福岡微分幾何研究会
  • Place of Presentation: 福岡大学
  • Year and Date: 2007-02-04
• [Presentation] 複素双曲線上の曲線の運動 (2007)
  • Author(s): 藤岡敦
  • Organizer: 部分多様体論・湯沢2007
  • Place of Presentation: 湯沢グランドホテル
  • Year and Date: 2007-01-22
• [Remarks]
  • URL: http://www.econ.hit-u.ac.jp/~koho/jpn/introduce/professor/MA_fujioka.html
• [Remarks]
  • URL: http://www.econ.hit-u.ac.jp/~koho/jpn/introduce/professor/MA_fujioka.html