Submanifolds and homogeneous curves

• Project/Area Number: 23540097
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Saga University
• Principal Investigator: MAEDA Sadahiro 佐賀大学, 工学(系)研究科(研究院), 教授 (40181581)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 微分幾何学 / 実超曲面論 / 等質実超曲面 / 線織実超曲面 / 測地線 / 円 / 接触形式 / 外微分 / 非平坦複素空間形 / 実超曲面 / 等長はめ込み / 型作用素 / 非等質実超曲面 / 測地球面 / ホップ超曲面 / リッチテンソル / イーター平行 / 極小 / 非平坦複素射影空間 / 構造テンソル / ホロ球面

Outline of Final Research Achievements

There are almost results related to real hypersurfaces in a nonflat complex space form which is either a complex projective space or a complex hyperbolic space. It is known that there does not exist a real hypersurface all of whose geodesics are mapped to circles in a nonflat complex space form. From this viewpoint we consider three real hypersurfaces in this ambient space. This result is a main theorem in this study. Another main theorem is a classification theorem of minimal ruled real hypersurfaces in a nonflat complex space form. Complex projective space admits just one minimal ruled real hypersurface. However Complex hyperbolic space admits three minimal ruled real hypersurfaces. This result depends on the sign of sectional curvatures of these ambient spaces. From this viewpoint this result is interesting.

Research Products

• [Journal Article] Congruence classes of minimal ruled real hypersurfaces in a nonflat complex space form (2014)
  • Author(s): 前田定廣、足立俊明、T. Bao
  • Journal Title: Hokkaido Math. J. Volume: Vol. 43 Pages: 1-14
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Hopf hypersurfaces with $\eta$-parallel Ricci tensors in a nonflat complex space form (2013)
  • Author(s): Sadahiro Maeda
  • Journal Title: Sci. Math. Japonicae Volume: 76 Pages: 449-456
  • Peer Reviewed
• [Journal Article] Characterizations of geodesic hyperspheres in a nonflat complex space form (2012)
  • Author(s): 前田定廣、足立俊明、Y.H. Kim
  • Journal Title: Glasgow Math. J. Volume: 32 Pages: 1-10
  • Peer Reviewed
• [Journal Article] Geometry of the horosphere in a complex hyperbolic (2011)
  • Author(s): Sadahiro Maeda
  • Journal Title: Differential geometry and its applications Volume: 29
  • Peer Reviewed
• [Presentation] 非平坦複素空間形内の線織実超曲面に関する注意 (2015)
  • Author(s): 前田定廣、足立俊明
  • Organizer: 日本数学会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-22
• [Presentation] 複素双曲型空間内の３つの等質実超曲面の特徴付け (2013)
  • Author(s): 前田 定廣
  • Organizer: Hot Topics Workshop on Differential geometry and Mathematical Physics
  • Place of Presentation: 韓国太田
  • Invited
• [Presentation] 複素双曲型空間内の３つの等質実超曲面の特徴付け
  • Author(s): 前田 定廣
  • Organizer: 日本数学会
  • Place of Presentation: 学習院大学
• [Presentation] 複素双曲型空間内のホロ球面の特徴付け
  • Author(s): 前田 定廣
  • Organizer: 日本数学会学会
  • Place of Presentation: 信州大学
• [Book] Differential geometry of submanifolds and its related topics (2013)
  • Author(s): Sadahiro Maeda,Yoshihiro Ohnita, Qing-Ming Cheng
  • Total Pages: 289
  • Publisher: World Sci 社