Research of submanifolds in symmetric spaces by usingthe infinite dimensional geometry and the complexification
| Project/Area Number |
21540095
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
KOIKE Naoyuki 東京理科大学, 理学部第一部数学科, 准教授 (00281410)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 部分多様体幾何 / リ-群作用 / 平均曲率流 / 対称空間 / 無限次元幾何 / 複素化 / 幾何学 |
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| Research Abstract |
Main results of this research are as follows.
(1) We showed that complex equifocal submanifolds in a symmetric space of non-compact type are congruent to principal orbits of Lie group actions called “Hermann action” under certain conditions.
(2) We showed that non-minimal equifocal submanifolds in a symmetric space of compact type collapse to their focal submanifolds along the mean curvature flow.
(3) We investigated the regularized mean curvature flow for invariant hypersurfaces in a Hilbert space equipped with a Hilbert Lie group free action and proved a certain kind of strongly convex preservability theorem for the flow.
(4) We classified hyperpolar actions on symmetric spaces of non-compact type under some conditions.
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Report
(5 results)
Research Products
(53 results)
