The symmetry and the homogeneity in pseudo-Riemannian geometry

• Project/Area Number: 20540067
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Ochanomizu University
• Principal Investigator: TSUKADA Kazumi Ochanomizu University, 大学院・人間文化創成科学研究科, 教授 (30163760)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 無限小等質空間 / 共形平坦等質ローレンツ多様体 / ホロ円曲面 / 共形平坦等ローレンツ多様体 / 左不変擬リーマン計量の測地的完備性 / 等質四元数擬ケーラー多様体 / 対称部分多様体

Research Abstract

We studied the following subjects on the symmetry and the homogeneity in pseudo-Riemannian geometry .We developed the classification problem of conformally flat homogeneous Lorentzian manifolds. For almost all types of the Ricci operators, we have solved the construction and the classification problem. We construct horocyclic surfaces in hyperbolic3-space associated with spacelike curves in the lightcone and classify their singularities using invariants of corresponding spacelike curves.

Research Products

• [Journal Article] Horocyclic surfaces in hyperbolic 3-space (2009)
  • Author(s): C.Takizawa K.Tsukada
  • Journal Title: Kyushu Journal of Mathematics 63 Pages: 269-284
  • NAID: 130000135283
  • Peer Reviewed
• [Journal Article] Horocyclic surfaces in hyperbolic 3-space (2009)
  • Author(s): C.Takizawa, K.Tsukada
  • Journal Title: Kyushu Journal of Mathematics 63 Pages: 269-284
  • NAID: 130000135283
  • Peer Reviewed
• [Presentation] Conformally flat homogeneous Lorentzian manifolds (2010)
  • Author(s): 本多恭子, 塚田和美
  • Organizer: International conference "Lie Transformation Groups and Complex Geometry"
  • Place of Presentation: Yuzawa, Niigata-Ken
  • Year and Date: 2010-09-29
• [Presentation] Conformally flat homogeneous Lorentzian manifolds (2010)
  • Author(s): 本多恭子、塚田和美
  • Organizer: 国際研究集会"Lie Transformation Groups and Complex Geometry"
  • Place of Presentation: 新潟県越後湯沢ホテルニューオオタニ
  • Year and Date: 2010-09-29
• [Presentation] Horocyclic surfaces in hyperbolic 3-spaces (2008)
  • Author(s): 塚田和美
  • Organizer: 部分多様体論・湯沢2008
  • Place of Presentation: 湯沢グランドホテル
  • Year and Date: 2008-11-28
• [Presentation] 擬リーマン多様体の等質性と曲率テンソル (2008)
  • Author(s): 塚田和美
  • Organizer: 新潟微分幾何学研究集会「微分幾何学と概複素構造」
  • Place of Presentation: 新潟大学
  • Year and Date: 2008-11-06
• [Presentation] 擬リーマン多様体の等質性と曲率テンソル (2008)
  • Author(s): 塚田 和美
  • Organizer: 新潟微分幾何学研究集会
  • Place of Presentation: 新潟大学
  • Year and Date: 2008-11-06
• [Presentation] n次元共形平坦等質ローレンツ多様体 (2008)
  • Author(s): 本多恭子, 塚田和美
  • Organizer: 第55回幾何学シンポジウム
  • Place of Presentation: 弘前大学
  • Year and Date: 2008-08-22