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Geometry of weakly reflective submanifolds

Research Project

Project/Area Number 20740044
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionOsaka 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 *help
¥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.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (38 results)

All 2011 2010 2009 2008 Other

All Journal Article (11 results) (of which Peer Reviewed: 7 results) Presentation (23 results) Remarks (4 results)

  • [Journal Article] Introduction to integral geometry in Riemannian homogeneous spaces, Proceedings of the 14th International Workshop on Differential Geometry and Related Fields2010

    • Author(s)
      Takashi Sakai
    • Journal Title

      Kyungpook National University, Taegue, Korea Vol.14

      Pages: 145-162

    • Related Report
      2010 Final Research Report
  • [Journal Article] Tight Lagrangian surfaces in S^2×S^22010

    • Author(s)
      Hiroshi Iriyeh, Takashi Sakai
    • Journal Title

      Geom.Dedicata 145, No.1

      Pages: 1-17

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lie-algebraic Characterization of tangentially degenerate orbits of s-representations2010

    • Author(s)
      Osamu Ikawa, Takashi Sakai, Hiroyuki Tasaki
    • Journal Title

      Differential Geom.Appl. 28, No.1

      Pages: 81-101

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lie algebraic characterization of tangentially degenerate orbits of s-representations2010

    • Author(s)
      O.Ikawa, T.Sakai, H.Tasaki
    • Journal Title

      Differential Geometry and its Applications

      Volume: 28 Pages: 81-101

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tight Lagrangian surfaces in S^2×S^22010

    • Author(s)
      H.Iriyeh, T.Sakai
    • Journal Title

      Geometry Dedicata

      Volume: 145 Pages: 1-17

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lie-algebraic characterization of tangentially degenerate orbits of s-representations2010

    • Author(s)
      O.Ikawa, T.Sakai, H.Tasaki
    • Journal Title

      Differential Geometry and its Applications 28

      Pages: 81-101

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weakly reflective submanifolds and austere submanifolds2009

    • Author(s)
      Osamu Ikawa, Takashi Sakai, Hiroyuki Tasaki
    • Journal Title

      J.Math.Soc.Japan. 61, No.2

      Pages: 437-481

    • NAID

      10024905762

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weakly reflective submanifolds and austere submanifolds2009

    • Author(s)
      O.Ikawa, T.Sakai, H.Tasaki
    • Journal Title

      Journal of the Mathematical Society of Japan 61

      Pages: 437-481

    • NAID

      10024905762

    • Related Report
      2009 Annual Research Report
    • 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 Fields2008

    • Author(s)
      Takashi Sakai
    • Journal Title

      Kyungpook National University, Taegue, Korea Vol.12

      Pages: 161-174

    • Related Report
      2010 Final Research Report
  • [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

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Tight Lagrangian surfaces in S^2×S^22008

    • Author(s)
      H. Iriyeh and T. Sakai
    • Journal Title

      OCAMI preprint series 08-7

      Pages: 1-16

    • Related Report
      2008 Annual Research Report
  • [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
    • Related Report
      2010 Final Research Report
  • [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
    • Related Report
      2010 Final Research Report
  • [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
    • Related Report
      2010 Annual Research Report
  • [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
    • Related Report
      2010 Annual Research Report
  • [Presentation] Tight Lagrangian Submanifolds in some homogeneous Kahler manifolds2010

    • 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
    • Related Report
      2009 Annual Research Report
  • [Presentation] Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere2010

    • Author(s)
      酒井高司
    • Organizer
      Workshop on Hypersurfaces Geometry and Integrable Systems
    • Place of Presentation
      東北大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Tight Lagrangian submanifolds in some homogeneous Kahler manifolds2010

    • 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
    • Related Report
      2010 Final Research Report
  • [Presentation] Introduction to integral geometry in Riemannian homogeneous spaces, International Mini-Workshop on Integral Geometry and Symmetric spaces2010

    • Author(s)
      Takashi Sakai
    • Organizer
      Kyungpook NationalUniversity
    • Place of Presentation
      Taegu, Korea, February
    • Related Report
      2010 Final Research Report
  • [Presentation] Introduction to integral geometry in Riemannian homogeneous spaces2010

    • Author(s)
      酒井高司
    • Organizer
      International Mini-Workshop on Integral Geometry and Symmetric Spaces
    • Place of Presentation
      Kyungpook National University
    • Related Report
      2009 Annual Research Report
  • [Presentation] Explicit expressions of kinematic formulae in Riemannian homogeneous spaces2009

    • 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
    • Related Report
      2009 Annual Research Report
  • [Presentation] Minimal surfaces with 3D-XplorMath and Maple2009

    • 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
    • Related Report
      2009 Annual Research Report
  • [Presentation] Absolutely area-minimizing cones over some minimal submanifolds in the sphere2009

    • 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
    • Related Report
      2009 Annual Research Report
  • [Presentation] Explicit expressions of Kinematic formulae in Riemannian homogeneous spaces2009

    • 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
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal surfaces with3D-XplorMath and Maple2009

    • 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
    • Related Report
      2010 Final Research Report
  • [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
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Absolutely area-minimizingcones over some minimal submanifolds in the sphere2009

    • 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
    • Related Report
      2010 Final Research Report
  • [Presentation] Absolutely area-minimizing cones over some minimal submanifolds in S^n2009

    • 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
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Tight Lagrangian surfaces in S^2×S^22009

    • 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
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [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
    • Related Report
      2008 Annual Research Report
  • [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
    • Related Report
      2008 Annual Research Report
  • [Presentation] Weakly reflective orbits and tangentially degenerate orbits of s-representations, One-Day Workshop on Differential Geometry2008

    • Author(s)
      Takashi Sakai
    • Organizer
      National Taiwan University
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      2008-04-01
    • Related Report
      2010 Final Research Report
  • [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
    • Related Report
      2010 Final Research Report
  • [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
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ

    • URL

      http://www.comp.tmu.ac.jp/tsakai/

    • Related Report
      2010 Final Research Report
  • [Remarks] 秋葉原微分幾何セミナー

    • URL

      http://tmugs.math.se.tmu.ac.jp/g-akihabara/

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.comp.tmu.ac.jp/tsakai/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.comp.tmu.ac.jp/tsakai/

    • Related Report
      2009 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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