Deepening and Evolution of Theory of Submanifolds and Harmonic Maps in Symmetric Spaces
| Project/Area Number |
18K03307
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Osaka Metropolitan University (2022)
Osaka City University (2018-2021) |
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Principal Investigator |
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| 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)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| 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)
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| 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 |
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| 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,
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| 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．
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Report
(6 results)
Research Products
(51 results)
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[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
Int'l Joint Research / Invited
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