Wente Torus in complex space forms

• Project/Area Number: 18540061
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: KENMOTSU Katsuei Tohoku University, 大学院・理学研究科, 名誉教授 (60004404)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,280,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥480,000); 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: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 微分幾何学 / 部分多様体 / 平均曲率ベクトル / 複素空間形 / 回転超曲面 / 平均曲率

Research Abstract

3次元ユークリッド空間内の平均曲率一定曲面論を拡張する目的で、本研究では複素2次元複素空間形内で平均曲率ベクトル場が平行な実2次元曲面の局所構造を研究した。その結果このような曲面はケーラー角度関数の性質によりI型とII型の2種類に分かれることを示した。
I型については曲面の構成法まで含めて完全な理解が得られた。II型の曲面については第一、第二基本形式が決定できたことによりそのような曲面の局所構造の解析をほぼ終了した。

Research Products

• [Journal Article] Rotational hypersurfaces of periodic mean curvature (2009)
  • Author(s): J. Dorfmeister, K. Kenmotsu
  • Journal Title: Differential Geometry and its Applications
  • Peer Reviewed
• [Journal Article] Rotational hypersurfaces of periodic mean curvature (2009)
  • Author(s): J. Dorfmeister
  • Journal Title: Differential Geometry and its Applications 10.1016/j. difgeo. 2009.03.010(オンライン出版)
  • Peer Reviewed
• [Journal Article] On a theorem by Hsiang and Yu (2008)
  • Author(s): J. Dorfmeister, K. Kenmotsu
  • Journal Title: Ann Glob Anal Geom 33 Pages: 245-252
  • Peer Reviewed
• [Journal Article] On a theorem by Hsiang and Yu (2008)
  • Author(s): J. Dormeister
  • Journal Title: Ann Glob Anal Geom 33 Pages: 245-252
  • Peer Reviewed
• [Journal Article] On a theorem by Hsiang and Yu (2007)
  • Author(s): J. Dorfmeister and K. Kenmotsu
  • Journal Title: Ann Glob Anal Geom(オン ライン出版) 10 Pages: 9083-9087
  • Peer Reviewed
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 剱持 勝衛
  • Organizer: COMCA2008
  • Place of Presentation: イキケ市 (チリー)
  • Year and Date: 2008-07-31
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 剱持 勝衛
  • Organizer: 数学科招待講演会
  • Place of Presentation: 広州市 中山大学 (中国)
  • Year and Date: 2008-05-26
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 劔持勝衛
  • Organizer: 中国・中山大学幾何学セミナー
  • Place of Presentation: 中国・広州市
  • Year and Date: 2008-05-26
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 剱持 勝衛
  • Organizer: 数学科招待講演会
  • Place of Presentation: サンパウロ大学数学科 (ブラジル)
  • Year and Date: 2008-03-07
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 劔持 勝衛
  • Organizer: 数学科招待講演会
  • Place of Presentation: サンパウロ大学数学科
  • Year and Date: 2008-03-07
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 剱持 勝衛
  • Organizer: 数学科招待講演会
  • Place of Presentation: セアラ大学数学科 (ブラジル)
  • Year and Date: 2008-02-22
• [Presentation] Rotational hypersurfaces of periodic mean curvature (2008)
  • Author(s): 劔持 勝衛
  • Organizer: 数学科招待講演会
  • Place of Presentation: セアラ大学数学科
  • Year and Date: 2008-02-22
• [Presentation] Surface of revolution with periodic mean curvature (2007)
  • Author(s): 剱持 勝衛
  • Organizer: Korea Ufniversity
  • Place of Presentation: ソウル (韓国)
  • Year and Date: 2007-12-20
• [Presentation] On a Theorem about Hsiang and Yu (2007)
  • Author(s): 剱持 勝衛
  • Organizer: 北京理工大学幾何学セミナー
  • Place of Presentation: 北京市 (中華人民共和国)
  • Year and Date: 2007-06-04
• [Presentation] On the Ricci condition of cmc-surfaces in complex space forms (2006)
  • Author(s): 剱持 勝衛
  • Organizer: 国際研究集会 "Methods of Integrable systems in Geometry"
  • Place of Presentation: ダーラム大学 (イギリス)
  • Year and Date: 2006-08-17
• [Presentation] On the Ricci condition of cmc-surfaces in complex space forms (2006)
  • Author(s): 剱持 勝衛
  • Organizer: 国際研究集会"Methods of Integrable systems in Geometry"
  • Place of Presentation: ダーラム大学(イギリス)
  • Year and Date: 2006-08-17
• [Presentation] Periodic meancurvature surfaces (2006)
  • Author(s): 剱持 勝衛
  • Organizer: 2006 Joint Seminar of The NSFC-KOSEF Scientific Cooperation Program
  • Place of Presentation: 瀋陽市 (中国)
• [Book] コンソーシアム「マス・フォア・インダストリ」第1回フォーラムCOE Lecture Note Vol.12 (2008)
  • Author(s): 西成活裕, Tobias Kretz, 三部幸治, 剱持勝衛, Tim Hoffman, 源田悦夫, 安倍直樹, Aurelie Lozano, 村田昇, 福本康秀
  • Publisher: Kyushu University
• [Remarks] ホームページ等
  • URL: http://www.math.tohoku.ac.jp/~kenmotsu
• [Remarks]
  • URL: http://www.math.tohoku.ac.jp/~kenmotsu/
• [Remarks]
  • URL: http://www.math.tohoku.ac.jp/~kenmotsu/
• [Remarks]
  • URL: http://www.math.tohoku.ac.jp/~kenmotsu/