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New Development of Submanifold Geometry and Harmonic Map Theory in Symmetric Spaces

Research Project

Project/Area Number 15K04851
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) 加藤 信  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)
TANAKA Makiko S.  東京理科大学, 理工学部, 教授 (20255623)
GUEST Martin  早稲田大学, 理工学術院, 教授 (10295470)
IRIYEH Hiroshi  茨城大学, 理学部, 准教授 (30385489)
KAJIGAYA Toru  東京電機大学, 工学部, 助教 (20749361)
Research Collaborator KOIKE Naoyuki  東京理科大学, 理学部, 教授 (00281410)
HASHIMOTO Kaname  大阪市立大学, 数学研究所, 専任研究所員 (10647837)
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords極小部分多様体 / ラグランジュ部分多様体 / 対称空間 / 調和写像 / 等径部分多様体 / 可積分系 / リー群 / モジュライ空間 / 微分幾何学 / 部分多様体 / フレアーホモロジー / 等質空間
Outline of Final Research Achievements

In this project we investigate submanifold geometry and harmonic map theory in symmetric spaces from the viewpoints of geometric variational problems, integrable systems, Lie theory of finite and infinite dimension, symplectic geometry: (1) Harmonic maps and integrable systems, (2) homogeneous submanifolds of special types, (3) Lagrangian submanifolds in Hermite symetric spaces, (5) isoparametric submanifolds of finite and infinite dimensions. Especially, based on our previous study on compact minimal Lagrangian submanifolds embedded in complex hyperquadrics obtained as Gauss images ofisoparametric hypersurfaces, we obtained and published a new result that if the Gauss images ofisoparametric hypersurfaces in the standard spheres are Hamiltonian non-displaceable except for three cases (g,m_1,m_2)=(3,1,1), (4,1,k) (k≧1),(6,1,1) in a joint work with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka. This result gives a link between classical differential geometry and modern symplectic geometry.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (29 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (4 results) Journal Article (6 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 4 results,  Open Access: 3 results,  Acknowledgement Compliant: 4 results) Presentation (14 results) (of which Int'l Joint Research: 7 results,  Invited: 11 results) Book (1 results) Remarks (3 results) Funded Workshop (1 results)

  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] 全南大学(韓国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] On Floer homology of the Gauss images of isoparametric hypersurfaces2017

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      “Hermitian-Grassmannian Submanifolds”, Springer Proceedings in Mathematics & Statistics

      Volume: 17 Issue: 07 Pages: 1-13

    • DOI

      10.1007/978-981-10-5556-0_20

    • ISBN
      9789811055553, 9789811055560
    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016861

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On classification of minimal orbits of the Hermann action  satisfying Koike's conditions (Joint work with Minoru Yoshida)2017

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of The 21st International Workshop on Hermitian Symmetric Spaces and Submanifolds

      Volume: 21 Pages: 1-15

    • Related Report
      2017 Annual Research Report
  • [Journal Article] On Floer homology of the Gauss images of isoparametric hypersurfaces2017

    • Author(s)
      Y.Ohnita
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: -

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] HAMILTONIAN NON-DISPLACEABILITY OF GAUSS IMAGES OF ISOPARAMETRIC HYPERSURFACES2016

    • Author(s)
      H. Iriyeh, H. Ma, R. Miyaoka, Y. Ohnita
    • Journal Title

      Bull. Lond. Math. Soc.

      Volume: 15 Issue: 12 Pages: 1-11

    • DOI

      10.1112/blms/bdw040

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016839

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Hamiltonian stability of the Gauss images of homogenous isoparametric hypersurfaces. II2015

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

      Tohoku Mathematical Journal

      Volume: 67 Pages: 195-246

    • NAID

      130007961932

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Geometry of Lagrangian submanifolds in complex hyperquadrics and the Gauss images of isoparametric hypersurfaces2015

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of The Nineteenth International Workshop on Hermitian-Grassmannian Submanifolds and Its Applications

      Volume: 19 Pages: 283-307

    • Related Report
      2015 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Presentation] Symmetries and moduli spaces for harmonic maps2018

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      International Conference “Geometry of Submanifolds and Integrable Systems”, The 15th OCAMI-RIRCM Joint Workshop & The 3rd OCAMI-KOBE-WASEDA Joint International Workshop
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of minimal orbits of the Hermann action satisfying Koike's conditions2017

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 21st International Workshop on Hermitian Symmetric Spaces and Submanifolds & The 14th RIRCM-OCAMI Joint Differential Geometry Workshop
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of minimal orbits of the Hermann action satisfying Koike's conditions2017

    • Author(s)
      大仁田義裕
    • Organizer
      福岡大学微分幾何研究集会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 小池の条件を満たすHermann作用の軌道の分類について2017

    • Author(s)
      大仁田義裕
    • Organizer
      部分多様体論・湯沢2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Approach from hypersurface geometry to the Floer theory on Lagrangian intersections , I(R.Miyaoka), II(Y.Ohnita)2017

    • Author(s)
      Reiko Miyaoka, Yoshihiro Ohnita
    • Organizer
      International Conference “Differential Geometry and Differential Equations:the influence of Mirror Symmetry and Physics”
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On Floer homology of the Gauss images of isoparametric hypersurfaces2017

    • Author(s)
      Y. Ohnita
    • Organizer
      Tohoku University Mini-Workshop
    • Place of Presentation
      東北大学 川井ホール(数理科学記念館) (宮城県仙台市)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On Floer homology of the Gauss images of isoparametric hypersurfaces2017

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 13th OCAMI-RIRCM Joint Differential Geometry Workshop on Submanifold Geometry and Lie Theory
    • Place of Presentation
      Osaka City University (大阪府大阪市)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 等径超曲面のガウス像のHamiltonian non-diplaceability2016

    • Author(s)
      入江博, Hui Ma, 宮岡礼子,大仁田義裕
    • Organizer
      日本数学会2016年度年会 幾何学分科会 一般講演
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
  • [Presentation] On Floer homology of the Gauss images of isoparametric hypersurfaces2016

    • Author(s)
      Y. Ohnita
    • Organizer
      The 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds & The 12th RIRCM-OCAMI Joint Differential Geometry Workshop
    • Place of Presentation
      Kyungpook National University (Korea)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] OT-FKM型等径超曲面について(サーベイ)2016

    • Author(s)
      大仁田義裕
    • Organizer
      水戸幾何小研究集会
    • Place of Presentation
      茨城大学理学部 (茨城県水戸市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Harmonic maps from Riemann surfaces into symetric spaces and their moduli spaces I & II2015

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      RIMS研究集会「低次元多様体モジュライ空間の幾何学」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2015-12-18
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces (joint work with H.Iriyeh, H.Ma, R.Miyaoka)2015

    • Author(s)
      大仁田義裕
    • Organizer
      福岡大学微分幾何研究会
    • Place of Presentation
      福岡大学セミナーハウス(福岡県福岡市)
    • Year and Date
      2015-11-01
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Harmonic maps into symmetric spaces and integrable system approach2015

    • Author(s)
      大仁田義裕
    • Organizer
      数理物理・幾何ミニワークショップ
    • Place of Presentation
      大阪市立大学(大阪府大阪市)
    • Year and Date
      2015-08-24
    • Related Report
      2015 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)
      大仁田義裕
    • Organizer
      RIMS研究集会「部分多様体論と種々の幾何構造 (Submanifold theory and geometric structures)」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2015-06-24
    • Related Report
      2015 Research-status Report
    • Invited
  • [Book] "Hermitian-Grassmannian Submanifolds", Daegu, Korea, July 20162017

    • Author(s)
      Young Jin Suh, Yoshihiro Ohnita, Jiazu Zhou, Byung Hak Kim, Hyunjin Lee
    • Total Pages
      360
    • Publisher
      Springer Proceedings in Mathematics and Statistics 203
    • ISBN
      9789811055553
    • Related Report
      2017 Annual Research Report
  • [Remarks] 大仁田研究室HP

    • Related Report
      2017 Annual Research Report
  • [Remarks] http://www.sci.osaka-cu.ac.jp/~ohnita/

    • Related Report
      2016 Research-status Report
  • [Remarks] http://www.sci.osaka-cu.ac.jp/~ohnita/

    • Related Report
      2015 Research-status Report
  • [Funded Workshop] Geometry of Submanifolds and Integrable Systems2018

    • Related Report
      2017 Annual Research Report

URL: 

Published: 2015-04-16   Modified: 2023-03-16  

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