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Research on special Lagrangian submanifolds in non-flat Calabi-Yau manifolds

Research Project

Project/Area Number 23740057
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionTokyo Metropolitan University

Principal Investigator

SAKAI Takashi  首都大学東京, 理工学研究科, 准教授 (30381445)

Project Period (FY) 2011 – 2014
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords微分幾何 / 対称空間 / Calabi-Yau多様体 / Lagrange部分多様体 / キャリブレーション / 複素旗多様体 / 対蹠集合 / カラビ‐ヤウ多様体 / ラグランジュ部分多様体 / 旗多様体
Outline of Final Research Achievements

We studied special Lagrangian submanifolds in Calabi-Yau manifolds. Moreover we investigated Floer homology and Hamiltonian volume minimizing properties of Lagrangian submanifolds, and we also investigated conical singularities on minimal submanifolds.
The cotangent bundles of compact rank one symmetric spaces admit complete Ricci flat Kahler metrics of cohomogeneity one due to M. Stenzel. Using the symmetry of the Stenzel metric, we constructed cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere by the moment map technique. Furthermore, we observed singularities and the asymptotic behavior of those special Lagrangian submanifolds.

Report

(4 results)
  • 2014 Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (19 results)

All 2014 2013 2012 2011 Other

All Journal Article (4 results) (of which Peer Reviewed: 3 results) Presentation (12 results) (of which Invited: 2 results) Remarks (3 results)

  • [Journal Article] 複素旗多様体内の実旗多様体の交叉の構造2014

    • Author(s)
      入江博,酒井高司,田崎博之
    • Journal Title

      数理解析研究所講究録

      Volume: 1880 Pages: 100-116

    • Related Report
      2013 Annual Research Report
  • [Journal Article] On the structure of the intersection of real flag manifolds in a complex flag manifold2013

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

      Advanced Studies in Pure Mathematics

      Volume: -

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] COHOMOGENEITY ONE SPECIAL LAGRANGIAN SUBMANIFOLDS IN THE COTANGENT BUNDLE OF THE SPHERE2012

    • Author(s)
      K.Hashimoto, T.Sakai
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 64 Issue: 1 Pages: 141-169

    • DOI

      10.2748/tmj/1332767344

    • NAID

      130005128507

    • ISSN
      0040-8735, 2186-585X
    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016749

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type2012

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

      Journal of Mathematical Society of Japan

      Volume: 掲載決定

    • NAID

      130003384667

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Minimal submanifolds in Riemannian manifolds2014

    • Author(s)
      Takashi Sakai
    • Organizer
      Mini-courses on area-minimizing varieties
    • Place of Presentation
      韓国, ソウル, Korea Institute for Advanced Study
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Antipodal structure of the intersection of real forms and its applications2014

    • Author(s)
      Takashi Sakai
    • Organizer
      Differential Geometry Seminar
    • Place of Presentation
      米国, カリフォルニア州, California University, Irvine
    • Related Report
      2013 Annual Research Report
  • [Presentation] 極小R空間上の面積最小錐2014

    • Author(s)
      酒井高司,大野晋司
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 複素旗多様体内の実旗多様体の交叉の構造2013

    • Author(s)
      入江博,酒井高司,田崎博之
    • Organizer
      部分多様体の微分幾何学の深化
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Special Lagrangian submanifolds with large symmetry2013

    • Author(s)
      酒井高司
    • Organizer
      GCOE小研究集会--Minimal submanifolds and mean curvature flow--
    • Place of Presentation
      KKR蔵王白銀荘
    • Related Report
      2012 Research-status Report
  • [Presentation] 複素旗多様体内の実旗多様体の交叉の構造2012

    • Author(s)
      入江博,酒井高司,田崎博之
    • Organizer
      日本数学会年会2012年度秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Antipodal structure of the intersection of real forms in a complex flag manifold2012

    • Author(s)
      Takashi Sakai
    • Organizer
      The 16th International Workshop on Differential Geometry
    • Place of Presentation
      Kyungpook National University, Taegu, Korea
    • Related Report
      2012 Research-status Report
  • [Presentation] Lagrangian Floer homology and its application to Hamiltonian volume minimizing property2012

    • Author(s)
      酒井高司
    • Organizer
      The 4th TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis(招待講演)
    • Place of Presentation
      国立台湾大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 複素二次超曲面の実形のHamilton体積最小性について2012

    • Author(s)
      酒井高司
    • Organizer
      シンプレクティック幾何と平均曲率流(招待講演)
    • Place of Presentation
      KKR蔵王白銀荘
    • Related Report
      2011 Research-status 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)
      酒井高司
    • Organizer
      理工学部数学科談話会(招待講演)
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 球面の余接束内の特殊Lagrange部分多様体2011

    • Author(s)
      酒井高司
    • Organizer
      部分多様体幾何とリー群作用(招待講演)
    • Place of Presentation
      東京理科大学森戸記念館
    • Related Report
      2011 Research-status Report
  • [Presentation] 複素二次超曲面の実形のHamilton体積最小性について2011

    • Author(s)
      酒井高司
    • Organizer
      部分多様体論・湯沢2011
    • Place of Presentation
      湯沢グランドホテル
    • Related Report
      2011 Research-status Report
  • [Remarks] 酒井高司のページ

    • URL

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

    • Related Report
      2013 Annual Research Report
  • [Remarks] TMUGS

    • URL

      http://tmugs.math.se.tmu.ac.jp/

    • Related Report
      2013 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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