• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Deepening and Evolution of Theory of Submanifolds and Harmonic Maps in Symmetric Spaces

Research Project

Project/Area Number 18K03307
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11020:Geometry-related
Research InstitutionOsaka Metropolitan University (2022)
Osaka City University (2018-2021)

Principal Investigator

Yoshihiro Ohnita  大阪公立大学, 大学院理学研究科, 教授 (90183764)

Co-Investigator(Kenkyū-buntansha) 加藤 信  大阪公立大学, 大学院理学研究科, 准教授 (10243354)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords微分幾何学 / 調和写像 / 部分多様体論 / 極小部分多様体 / 等径部分多様体 / リー群 / 対称空間 / 可積分系 / 幾何学的変分問題 / 調和写像論 / ラグランジュ部分多様体 / リー理論 / 部分多様体 / フレアーホモロジー
Outline of Final Research Achievements

In this project we promote further research in differential geometry of submanifolds and harmonic maps in symmetric spaces. R-spaces are important R-spaces are important compact homogeneous spaces which provide all of homogeneous isoparametric submanifolds and their focal submanifolds in finite dimensional Euclidean spaces. Each R-space is known to be canonically embedded in a K\”ahler C-space as a totally geodesic Lagrangian submanifold.
We studied geometry of R-spaces as Lagrangian submanifolds. And we showed several new results such as a new proof from the viewpoint of R-spaces for the classification theorem (Nakagawa-Takagi, 1979) of complex submanifolds with parallel second fundamental form in complex projective spaces. We are also steadily promoting joint works on geometry and topology of the Gauss images of isoparametric hypersurfaces and harmonic map theory related to integrable systems,

Academic Significance and Societal Importance of the Research Achievements

幾何学,とくに微分幾何学の分野において,対称空間に付随して構成されるコンパクト等質空間「R-空間」が,有限次元および無限次等径部分多様体理論においても重要な役割をしており,シンプレクティック幾何学のラグランジュ部分多様体の側面からも豊かな性質をもっていることを示すものであり,また新たな研究を示唆するものである.また,微分幾何学において重要な対象である高次元極小部分多様体と多様体の種々の幾何構造との関係について幾つもの新しい結果を与えていてる.今回の本研究課題の研究成果は,部分多様体論から微分幾何学の進展と今後の研究の方向性に寄与するものである.

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (51 results)

All 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (10 results) Journal Article (7 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 4 results,  Open Access: 6 results) Presentation (21 results) (of which Int'l Joint Research: 13 results,  Invited: 21 results) Book (1 results) Remarks (5 results) Funded Workshop (7 results)

  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] 全南大学(韓国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] 全南大学校(韓国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] 全南大学校(韓国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] 全南大学(韓国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] 清華大学(中国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] 全南大学/慶北国立大学(韓国)

    • Related Report
      2018 Research-status Report
  • [Journal Article] 等径部分多様体に関連した部分多様体の幾何学2022

    • Author(s)
      大仁田 義裕
    • Journal Title

      OCAMI Preprint Series

      Volume: 21 Issue: 15 Pages: 1-11

    • DOI

      10.24544/ocu.20220328-001

    • Year and Date
      2022-03-28
    • Related Report
      2021 Research-status Report
  • [Journal Article] Parallel K\"ahler submanifolds and R-spaces2022

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Contemporary Mathematics

      Volume: 777

    • Related Report
      2022 Annual Research Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Regularity of ends of zero mean curvature surfaces in 𝐑<sup>2,1</sup>2022

    • Author(s)
      aoya Ando,Kohei Hamada,Kaname Hashimoto,Shin Kato
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 74 Issue: 4 Pages: 1295-1334

    • DOI

      10.2969/jmsj/85018501

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Canonical connections of a Sasakian manifold and invariant submanifolds with parallel second fundamental form2021

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of The 23rd International Differential Geometry Workshop on Submanifolds in Homogeneous Spaces and Related Topics

      Volume: 23

    • Related Report
      2021 Research-status Report
    • Open Access
  • [Journal Article] Nonorientable minimal surfaces with catenoidal ends2020

    • Author(s)
      Kohei Hamada and Shin Kato
    • Journal Title

      Annali di Matematica Pura ed Applicata

      Volume: - Issue: 4 Pages: 1573-1603

    • DOI

      10.1007/s10231-020-01048-4

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] LAGRANGIAN GEOMETRY OF THE GAUSS IMAGES OF ISOPARAMETRIC HYPERSURFACES IN SPHERES2019

    • Author(s)
      Reiko Miyaoka and Yoshihiro Ohnita
    • Journal Title

      Complex Manifolds

      Volume: 18 Issue: 07 Pages: 1-19

    • DOI

      10.1515/coma-2019-0013

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016870

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Geometry of R-spaces canonically embedded in Kaehler C-spaces as Lagrangian submanifolds2019

    • Author(s)
      Yoshihiro Ohnita
    • Journal Title

      Proceedings of the 22nd International Workshop on Differental Geometry of Submanifolds in Symmetric Spaces & Related Problems

      Volume: 22 Pages: 116-132

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Presentation] Minimal Submanifolds, Harmonic Maps and Isoparametric Submanifolds2023

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      13th MSJ-SI "Differential Geometry and Integrable Systems" 3rd Shot
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Geometry of Lagrangian submanifolds and isoparametric submanifolds2023

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Mini-workshop : Global Analysis and Geometry
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 曲がった面を“測る”ことから始まる幾何学 ‐「多様体」の数学‐2022

    • Author(s)
      大仁田義裕
    • Organizer
      大阪公立大学の研究者の世界 第8回ACADEMIC CAFE
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 等径部分多様体に関連した部分多様体の幾何学2022

    • Author(s)
      大仁田義裕
    • Organizer
      第3回水戸幾何小研究集会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Parallel K\"ahler submanifolds and R-spaces2021

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 23rd International Differential Geometry Workshop on Submanifolds in Homogeneous Spaces and Related Topics & the 19th RIRCM-OCAMI Joint Differential Geometry Workshop (online)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 等径部分多様体に関連した部分多様体の幾何学2021

    • Author(s)
      大仁田義裕
    • Organizer
      第68回幾何学シンポジウム(オンライン)全体講演
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Higher dimensional generalization of the Chiang Lagrangian and totally complex submanifolds2021

    • Author(s)
      J.-T. Cho, K. Hashimoto and Y. Ohnita
    • Organizer
      OCAMI workshop on Submanifolds of Symmetric Spaces and their Time Evolutions (online)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 平均曲率 0 曲面の双複素拡張と平面型 end の正則2020

    • Author(s)
      加藤信
    • Organizer
      第 67 回幾何学シンポジウム(オンライン)
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces2019

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Conference "Variational problems and the geometry of submanifolds" (CIRM, 27-31 May, 2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Lagrangian geometry of the Gauss images of isoparametric hypersurfaces2019

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      2019 Workshop on the Isoparametric Theory (Beijing Normal Univ., June 2-6, 2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces2019

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 22nd International Workshop on Differential Geometry of Submanifolds in Symmetric Spaces and Related Problems (Kyungpook Natl. Univ., Jul. 31-Aug. 5, 2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 等径超曲面論入門2019

    • Author(s)
      大仁田 義裕
    • Organizer
      東京理科大学集中講義(2019年9月23,24,26,27日,組織:小池直之教授)
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces2019

    • Author(s)
      大仁田 義裕
    • Organizer
      第5回神楽坂微分幾何学セミナー(東京理科大学 神楽坂キャンパス,2019年9月28日)
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces2019

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Variational Problems in Geometry and Mathematical Physics, UK-Japan Winter School 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces2019

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Special talks organized by Professor Hui Ma (Tsinghua Umiversity)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Minimal Maslov number of R-spaces canonically embedded in Einstein-Kaehler C-spaces2019

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      The 2nd International Conference "Geometry of Submanifolds and Integrable Systems" (2019.3.22-3.26)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres2018

    • Author(s)
      Reiko Miyaoka and Yoshihiro Ohnita
    • Organizer
      The 5th Workshop on "Complex Geometry and Lie Groups"
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Geometry of Harmonic Maps and Integrable System Approach (1), (2)2018

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Mini-Workshop on Geometry and Mathematical Science
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 小池の条件を満たすHermann作用の極小軌道の分類について2018

    • Author(s)
      大仁田義裕
    • Organizer
      部分多様体幾何とリー群作用 2018 (2018年9月3日-4日)
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Lagrangian geometry of the Gauss images of isoparametric hypersurfaces2018

    • Author(s)
      Yoshihiro Ohnita
    • Organizer
      Special Session "Riemannian Geometry and related Topics", 2018 Joint Meeting of the Korean Mathematical Society and the Germany Mathematical Society
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] アインシュタイン-ケーラーC-空間に標準的に埋め込まれたR-空間の最小マスロフ数2018

    • Author(s)
      大仁田義裕
    • Organizer
      水戸幾何セミナー (2018年12月7日)
    • Related Report
      2018 Research-status Report
    • Invited
  • [Book] Proceedings of The 22nd International Workshop on Differential Geometry and Submanifolds in Symmetric Spaces and Related Problems2019

    • Author(s)
      Young Jin Suh, Yoshihiro Ohnita, Jiazu Zhou, Byung Hak Kim, Hyunjin Lee (Editors)
    • Total Pages
      278
    • Publisher
      Kyungpook National University (Daegu)
    • Related Report
      2019 Research-status Report
  • [Remarks] 大阪公立大学 理学研究科 数学専攻 微分幾何学 大仁田研究室

    • URL

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

    • Related Report
      2022 Annual Research Report
  • [Remarks] 大仁田研究室HP

    • Related Report
      2021 Research-status Report
  • [Remarks] 大仁田研究室HP

    • Related Report
      2020 Research-status Report
  • [Remarks] www.sci.osaka-cu.ac.jp/~ohnita/

    • Related Report
      2019 Research-status Report
  • [Remarks] 大仁田研究室HP

    • Related Report
      2018 Research-status Report
  • [Funded Workshop] The 3rd Shot of The 13th MSJ-SI "Differential Geometry and Integrable Systems"2023

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Mini-Workshop on Integrable Geometry and Related Topics at Tokushima2022

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] The 5th International Workshop Geometry of Submanifolds and Integrable Systems2022

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] RIMS Review Seminar ”Symmetry and Stability in Differential Geometry of Surfaces”2022

    • Related Report
      2021 Research-status Report
  • [Funded Workshop] RIMS Symposium "The 4th International Workshop Geometry of Submanifolds and Integrable Systems"2022

    • Related Report
      2021 Research-status Report
  • [Funded Workshop] 13th MSJ-SI“Differential Geometry and Integrable Systems”(First Shot)2022

    • Related Report
      2021 Research-status Report
  • [Funded Workshop] The 18th OCAMI-RIRCM Joint Differential Geometry Workshop "Differential Geometry of Submanifolds in Symmetric Spaces and Related Problems"2019

    • Related Report
      2019 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi