| Project/Area Number |
26400073
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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 | Tokyo Metropolitan University |
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Principal Investigator |
SAKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445)
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| Co-Investigator(Renkei-kenkyūsha) |
OHNITA Yoshihiro 大阪市立大学, 理学研究科, 教授 (90183764)
AKAHO Manabu 首都大学東京, 理工学研究科, 准教授 (30332935)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Lagrange部分多様体 / 極小部分多様体 / 対称空間 / 等質空間 / 二重調和写像 / 複素旗多様体 / 幾何学 |
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| Outline of Final Research Achievements |
In this research project, we studied variational problems for submanifolds in Riemannian manifolds using Lie group actions.
We studied the Lagrangian intersection of two real flag manifolds in a complex flag manifold. Then we showed that the intersection is an antipodal set of a complex flag manifold, if the intersection is discrete. We also studied biharmonic submanifolds in compact symmetric spaces. We gave a necessary and sufficient condition for orbits of commutative Hermann actions to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we constructed a great many examples of proper biharmonic homogeneous submanifolds in compact symmetric spaces, moreover we obtain some classifications.
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