Geometry of weakly reflective submanifolds

• Project/Area Number: 20740044
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Osaka City University
• Principal Investigator: SAKAI Takashi Osaka City University, 大学院・理工学研究科, 助教 (30381445)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 微分幾何学 / 極小部分多様体 / 等質空間 / 対称空間 / 幾何学

Research Abstract

We studied weakly reflective submanifolds. We constructed cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere and observed their singularities and asymptotic behavior. We obtained a deformation of a special Lagrangian submanifold which is given as the conormal bundle of a weakly reflective submanifold in the sphere concretely. We also studied global tightness and the Floer homology of real forms of Hermitian symmetric spaces of compact type.

Research Products

• [Journal Article] Introduction to integral geometry in Riemannian homogeneous spaces, Proceedings of the 14th International Workshop on Differential Geometry and Related Fields (2010)
  • Author(s): Takashi Sakai
  • Journal Title: Kyungpook National University, Taegue, Korea Vol.14 Pages: 145-162
• [Journal Article] Tight Lagrangian surfaces in S^2×S^2 (2010)
  • Author(s): Hiroshi Iriyeh, Takashi Sakai
  • Journal Title: Geom.Dedicata 145, No.1 Pages: 1-17
  • Peer Reviewed
• [Journal Article] Lie-algebraic Characterization of tangentially degenerate orbits of s-representations (2010)
  • Author(s): Osamu Ikawa, Takashi Sakai, Hiroyuki Tasaki
  • Journal Title: Differential Geom.Appl. 28, No.1 Pages: 81-101
  • Peer Reviewed
• [Journal Article] Lie algebraic characterization of tangentially degenerate orbits of s-representations (2010)
  • Author(s): O.Ikawa, T.Sakai, H.Tasaki
  • Journal Title: Differential Geometry and its Applications Volume: 28 Pages: 81-101
  • Peer Reviewed
• [Journal Article] Tight Lagrangian surfaces in S^2×S^2 (2010)
  • Author(s): H.Iriyeh, T.Sakai
  • Journal Title: Geometry Dedicata Volume: 145 Pages: 1-17
  • Peer Reviewed
• [Journal Article] Lie-algebraic characterization of tangentially degenerate orbits of s-representations (2010)
  • Author(s): O.Ikawa, T.Sakai, H.Tasaki
  • Journal Title: Differential Geometry and its Applications 28 Pages: 81-101
  • Peer Reviewed
• [Journal Article] Weakly reflective submanifolds and austere submanifolds (2009)
  • Author(s): Osamu Ikawa, Takashi Sakai, Hiroyuki Tasaki
  • Journal Title: J.Math.Soc.Japan. 61, No.2 Pages: 437-481
  • NAID: 10024905762
  • Peer Reviewed
• [Journal Article] Weakly reflective submanifolds and austere submanifolds (2009)
  • Author(s): O.Ikawa, T.Sakai, H.Tasaki
  • Journal Title: Journal of the Mathematical Society of Japan 61 Pages: 437-481
  • NAID: 10024905762
  • Peer Reviewed
• [Journal Article] Weakly reflective orbits and tangentially degenerate orbits of s-representations Proceedings of the 12th International Workshop on Differential Geometry and Related Fields (2008)
  • Author(s): Takashi Sakai
  • Journal Title: Kyungpook National University, Taegue, Korea Vol.12 Pages: 161-174
• [Journal Article] 3D-XplorMathの開発と教育利用について (2008)
  • Author(s): 酒井高司
  • Journal Title: 数式処理Bulletin of JSSAC 15 Pages: 55-61
  • NAID: 10023902535
• [Journal Article] Tight Lagrangian surfaces in S^2×S^2 (2008)
  • Author(s): H. Iriyeh and T. Sakai
  • Journal Title: OCAMI preprint series 08-7 Pages: 1-16
• [Presentation] コンパクト型Hermite対称空間の二つの実形の対のFloerホモロジー (2011)
  • Author(s): 入江博, 酒井高司, 田崎博之
  • Organizer: 日本数学会年会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-20
• [Presentation] 球面の余接束内の余等質性1の特殊Lagrange部分多様体 (2011)
  • Author(s): 橋本要, 酒井高司
  • Organizer: 日本数学会年会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-20
• [Presentation] コンパクト型Hermite対称空間の二つの実形の対のFloerホモロジー (2011)
  • Author(s): 入江博, 酒井高司, 田崎博之
  • Organizer: 日本数学会2011年度年会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-20
• [Presentation] 球面の余接束内の余等質性1の特殊Lagrange部分多様体 (2011)
  • Author(s): 橋本要, 酒井高司
  • Organizer: 日本数学会2011年度年会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-20
• [Presentation] Tight Lagrangian Submanifolds in some homogeneous Kahler manifolds (2010)
  • Author(s): 酒井高司
  • Organizer: TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis
  • Place of Presentation: National Taiwan University
  • Year and Date: 2010-03-21
• [Presentation] Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere (2010)
  • Author(s): 酒井高司
  • Organizer: Workshop on Hypersurfaces Geometry and Integrable Systems
  • Place of Presentation: 東北大学
• [Presentation] Tight Lagrangian submanifolds in some homogeneous Kahler manifolds (2010)
  • Author(s): Takashi Sakai
  • Organizer: The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis
  • Place of Presentation: National Taiwan University, Taipei, Taiwan
• [Presentation] Introduction to integral geometry in Riemannian homogeneous spaces, International Mini-Workshop on Integral Geometry and Symmetric spaces (2010)
  • Author(s): Takashi Sakai
  • Organizer: Kyungpook NationalUniversity
  • Place of Presentation: Taegu, Korea, February
• [Presentation] Introduction to integral geometry in Riemannian homogeneous spaces (2010)
  • Author(s): 酒井高司
  • Organizer: International Mini-Workshop on Integral Geometry and Symmetric Spaces
  • Place of Presentation: Kyungpook National University
• [Presentation] Explicit expressions of kinematic formulae in Riemannian homogeneous spaces (2009)
  • Author(s): 酒井高司
  • Organizer: 2009 Joint Meeting of the Korean Mathematical Society and the American Mathematical Society
  • Place of Presentation: Ewha Womans University
  • Year and Date: 2009-12-16
• [Presentation] Minimal surfaces with 3D-XplorMath and Maple (2009)
  • Author(s): 酒井高司
  • Organizer: 計算機を用いた数学研究
  • Place of Presentation: 京都大学
  • Year and Date: 2009-12-11
• [Presentation] Absolutely area-minimizing cones over some minimal submanifolds in the sphere (2009)
  • Author(s): 酒井高司
  • Organizer: 部分多様体幾何とリー群作用
  • Place of Presentation: 東京理科大学
  • Year and Date: 2009-09-08
• [Presentation] Explicit expressions of Kinematic formulae in Riemannian homogeneous spaces (2009)
  • Author(s): Takashi Sakai
  • Organizer: 2009 Joint Meeting of the Korean Mathematical Society and the American Mathematical Society
  • Place of Presentation: Ewha Womans University, Seoul, Korea
• [Presentation] Minimal surfaces with3D-XplorMath and Maple (2009)
  • Author(s): 酒井高司
  • Organizer: 計算機を用いた数学研究
  • Place of Presentation: 京都大学
• [Presentation] 旗多様体の実形の大域的タイト性 (2009)
  • Author(s): 酒井高司
  • Organizer: 部分多様体論・湯沢2009
  • Place of Presentation: 湯沢グランドホテル
• [Presentation] Absolutely area-minimizingcones over some minimal submanifolds in the sphere (2009)
  • Author(s): 酒井高司
  • Organizer: 部分多様体幾何とリー群作用
  • Place of Presentation: 東京理科大
• [Presentation] Absolutely area-minimizing cones over some minimal submanifolds in S^n (2009)
  • Author(s): 酒井高司
  • Organizer: 曲線と曲面の変分問題と関連する話題
  • Place of Presentation: 奈良女子大学
• [Presentation] Tight Lagrangian surfaces in S^2×S^2 (2009)
  • Author(s): 酒井高司
  • Organizer: 可積分系と幾何学の融合
  • Place of Presentation: 東北大学
• [Presentation] 弱鏡映部分多様体とその周辺の話題 (2008)
  • Author(s): 酒井高司
  • Organizer: 日本数学会秋季総合分科会 (幾何学分科会特別講演)
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] 複素球面内の特殊Lagrange部分多様体の構成について (2008)
  • Author(s): 酒井高司
  • Organizer: 第55回幾何学シンポジウム
  • Place of Presentation: 弘前大学
  • Year and Date: 2008-08-24
• [Presentation] Weakly reflective orbits and tangentially degenerate orbits of s-representations, One-Day Workshop on Differential Geometry (2008)
  • Author(s): Takashi Sakai
  • Organizer: National Taiwan University
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2008-04-01
• [Presentation] 弱鏡映部分多様体とその周辺の話題 (2008)
  • Author(s): 酒井高司
  • Organizer: 日本数学会秋季総合分科会(幾何学分科会特別講演)
  • Place of Presentation: 東京工業大学
• [Presentation] 複素球面内の特殊Lagrange部分多様体の構成について (2008)
  • Author(s): 酒井高司
  • Organizer: 幾何学シンポジウム
  • Place of Presentation: 弘前大学
• [Remarks] ホームページ
  • URL: http://www.comp.tmu.ac.jp/tsakai/
• [Remarks] 秋葉原微分幾何セミナー
  • URL: http://tmugs.math.se.tmu.ac.jp/g-akihabara/
• [Remarks]
  • URL: http://www.comp.tmu.ac.jp/tsakai/
• [Remarks]
  • URL: http://www.comp.tmu.ac.jp/tsakai/