| Project/Area Number |
15K04851
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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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| Research Field |
Geometry
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| Research Institution | Osaka City University |
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Principal Investigator |
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| 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)
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| 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)
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| 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)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| 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)
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| 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 |
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| 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.
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