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Research on submanifold geometry and harmonic map theory in symmetric spaces

Research Project

Project/Area Number 24540090
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionOsaka City University

Principal Investigator

OHNITA Yoshihiro  大阪市立大学, 大学院理学研究科, 教授 (90183764)

Co-Investigator(Kenkyū-buntansha) KATO Shin  大阪市立大学, 大学院理学研究科, 准教授 (10243354)
Co-Investigator(Renkei-kenkyūsha) SAKAI Takashi  首都大学東京, 大学院理工学研究科, 准教授 (30381445)
GUEST Martin  早稲田大学, 理工学術院, 教授 (10295470)
KOIKE Naoyuki  東京理科大学, 理学部, 教授 (00281410)
TANAKA Makiko S.  東京理科大学, 理工学部, 教授 (20255623)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords部分多様体論 / 極小部分多様体 / ラグランジュ部分多様体 / 対称空間 / 等径超曲面 / 調和写像 / 可積分系 / 微分幾何学 / リー理論 / 部分多様体
Outline of Final Research Achievements

In this project, from the viewpoints of geometric variational problems, integrable systems, Lie theory, symplectic geometry, we promoted to study harmonic maps in symmetric spaces and integrable systems, Hamiltonian stability of Lagrangian submanifolds, minimal submanifold theory, Lagrangian submanifolds related to isoparametric hypersurfaces, isoparametric submanifolds of finite and infinite dimensions. Especially, we has published our results on the property and structure of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics obtained as the Gauss images of isoparametric hypersurfaces (joint work with Hui Ma), such as the formula of minimal Maslov number, complete determination of Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces and so on. More recently we obtain new results on Hamiltonian non-displaceability of the Gauss images of isoparametric hypersurfaces in another joint work with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka.

Report

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

    (34 results)

All 2015 2014 2013 2012 Other

All Journal Article (9 results) (of which Peer Reviewed: 7 results,  Open Access: 1 results,  Acknowledgement Compliant: 2 results) Presentation (21 results) (of which Invited: 21 results) Book (2 results) Remarks (2 results)

  • [Journal Article] Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces, II2015

    • Author(s)
      Hui Ma and Yoshihiro Ohnita
    • Journal Title

      Tohoku Mathematical Journal

      Volume: -

    • NAID

      130007961932

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces, I2014

    • Author(s)
      Hui Ma and Yoshihiro Ohnita
    • Journal Title

      Journal of Differential Geometry

      Volume: 97 Pages: 275-348

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Geometry of Lagrangian submanifolds related to isoparametric hypersurfaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics

      Volume: 106 Pages: 117-127

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Differential Geometry of Submanifolds and its Related Topics

      Volume: - Pages: 60-81

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces. II2014

    • Author(s)
      Hui Ma and Yoshihiro Ohnita
    • Journal Title

      Tohoku Mathematical Journal

      Volume: -

    • NAID

      130007961932

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On intersections of the Gauss images of isoparametric hypersurfaces2013

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of The Seventeenth International Workshop on Differential Geometry and Related Fields

      Volume: 17 Pages: 201-213

    • Related Report
      2013 Research-status Report
  • [Journal Article] Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces. I2013

    • Author(s)
      Hui Ma and Yoshihiro Ohnita
    • Journal Title

      Journal of Differential Geometry

      Volume: 95 Pages: 1-74

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces2013

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of the workshop on Differential Geometry of Submanifolds and its related topics Saga

      Volume: -

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Certain compact homogeneous Lagrangian submanifolds in Hermitian symmetric spaces2012

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of The Sixteenth International Workshop on Differential Geometry and Related Fields

      Volume: 16 Pages: 225-240

    • Related Report
      2012 Research-status Report
  • [Presentation] Lagrangian intersection theory of the Gauss images of isoparametric hypersurfaces (ioint work with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka)2015

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      第9回大阪市立大学数学研究所-慶北国立大学 Hermitian-Grassmann Research Group 共催 微分幾何学ワークショップ 「部分多様体幾何学とリー理論」
    • Place of Presentation
      大阪市立大学(大阪府・大阪市)
    • Year and Date
      2015-02-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Geometry of Lagrangian submanifolds related to isoparametric hypersurfaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Workshop on LAGRANGIAN SUBMANIFOLDS AND RELATED TOPICS
    • Place of Presentation
      Department of Mathematics, University of Milano, Milano, Italy
    • Year and Date
      2014-12-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Gauge-theoretic approach to harmonic maps and subspaces in moduli spaces (joint work with Mariko Mukai-Hidano)2014

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Japan-Taiwan workshop on "Moduli spaces of flat connections on surfaces and related topics"
    • Place of Presentation
      早稲田大学 西早稲田キャンバス(東京都・新宿区)
    • Year and Date
      2014-11-15
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Geometry of Lagrangian Submanifolds related to Isoparametric Hypersurfaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      2014 ICM Satellite Conference & the 18th International Workshop on Real and Complex Submanifolds
    • Place of Presentation
      National Institute for Mathematical Sciences, Daejeon, Korea
    • Year and Date
      2014-08-11
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Geometry of Lagrangian Submanifolds related to Isoparametric Hypersurfaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      AKOOS-PNU International Conference 2014
    • Place of Presentation
      釜山国立大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Geometry of the Gauss images ofisoparametric hypersurfaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      第2回日本・スペイン幾何学研究集会
    • Place of Presentation
      東京工業大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Geometry of Lagrangian submanifolds related to isoparametric hypersurfaces2014

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Seminar of Differential Geometry (host: Professor Chuu-Lian Terng)
    • Place of Presentation
      Department of Mathematics, University of California・Irvine, USA
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Geometry of Lagrangian Submanifolds related to Isoparametric Hypersurfaces2013

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 2nd Pacific Rim Mathematical Association Congress (PRIMA 2013)
    • Place of Presentation
      Shanghai Jiao Tong University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Hamiltonian Stability Problem of Lagrangian Submanifols in Kaehler Manifolds I,II,III2013

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      GeoQuant 2013 Summer School
    • Place of Presentation
      ESI, Vienna
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On intersections of the Gauss images of isoparametric hypersurfaces2013

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      第17回慶北国立大学微分幾何学国際ワークショップ 兼 第7回慶北国立大学 Grassmann Research Group-大阪市立大学数学研究所共催微分幾何学ワークショップ
    • Place of Presentation
      韓国・National Institute for Mathematical Science
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On intersections of the Gauss images of isoparametric hypersurfaces2013

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      福岡大学微分幾何学研究会“Geometry and Something”
    • Place of Presentation
      福岡大学セミナーハウス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On the intersection of the Gauss images of isoparametric hypersurfaces2013

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      清華大学数学科学系 セミナー講演
    • Place of Presentation
      清華大学数学科学系
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 対称空間の部分多様体の微分幾何

    • Author(s)
      大仁田義裕
    • Organizer
      研究集会「部分多様体の微分幾何学及び関連課題」 --前田定廣先生還暦記念研究集会--
    • Place of Presentation
      佐賀大学理工学部
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] エルミート対称空間の等質ラグランジュ部分多様体とハミルトン安定性問題

    • Author(s)
      大仁田義裕
    • Organizer
      研究集会「部分多様体幾何とリー群作用 2012」
    • Place of Presentation
      東京理科大学森戸記念館第1フォーラム
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Certain compact homogeneous Lagrangian submanifolds in Hermitian symmetric spaces

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 16th Kyungpoosk National University International Workshop on Differential Geometry Workshop
    • Place of Presentation
      Kyungpook National University, Korea
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A construction of certain Lagrangian submanifolds in Hermitian symmetric spaces

    • Author(s)
      大仁田義裕
    • Organizer
      福岡大学微分幾何学研究会 "Geometry and Something
    • Place of Presentation
      福岡大学セミナーハウス
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A construction of certain Lagrangian submanifolds in complex projective spaces

    • Author(s)
      大仁田義裕
    • Organizer
      研究集会「部分多様体論・湯沢2012」
    • Place of Presentation
      湯沢グランドホテル
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Geometry of Lagrangian submanifolds related to isoparametric hypersurfaces

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Symplectic Geometry and Mathematical Physics
    • Place of Presentation
      Beijing International Center for Mathematical Research, P. R. China
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Willmore予想に対する可積分系アプローチ(1),(2)

    • Author(s)
      大仁田義裕
    • Organizer
      研究会「多様体上の変分問題と周辺領域」-Willmore曲面について-
    • Place of Presentation
      山口県健康づくりセンター
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Geometry of Lagrangian submanifolds related to isoparametric hypersurfaces

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      KCL/UCL Geometry Seminar (King's College London/University College London joint geometry seminar)
    • Place of Presentation
      University College London, England
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] エルミート対称空間のラグランジュ部分多様体の微分幾何

    • Author(s)
      大仁田義裕
    • Organizer
      東北大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
    • Invited
  • [Book] "Real and Complex Submanifolds", Daejeon, Korea, August 20142014

    • Author(s)
      Young Jin Suh, Juergen Berndt, Yoshihiro Ohnita, Byung Hak Kim, Hyunjin Lee (Editors)
    • Total Pages
      526
    • Publisher
      Springer Proceedings in Mathematics and Statistics 106
    • Related Report
      2014 Annual Research Report
  • [Book] Differential Geometry of Submanifolds and its Related Topics2014

    • Author(s)
      S. Maeda, Y. Ohnita, Q.-M. Cheng
    • Total Pages
      289
    • Publisher
      World Scientific Publishing Co. Pte. Ltd.
    • Related Report
      2013 Research-status Report
  • [Remarks] 大仁田研究室

    • URL

      http://www.sci.osaka-cu.ac.jp/~ohnita/

    • Related Report
      2013 Research-status Report
  • [Remarks] 大仁田研究室

    • URL

      http://www.sci.osaka-cu.ac.jp/~ohnita/

    • Related Report
      2012 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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