Research of submanifolds and mean curvature flows in symmetric spaces by using the infinite dimensional geometry and the complexification
| Project/Area Number |
25400076
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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 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, 教授 (00281410)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 部分多様体幾何 / 無限次元幾何 / 平均曲率流 / リー群作用 / 対称空間 / 部分多様体の複素化 / 等焦部分多様体 / 無限次元等径部分多様体 / 対称空間の複素化 / Polar作用 / 体積を保存する平均曲率流 / 正則化された平均曲率流 / ヒルベルト空間 / 等径部分多様体 / 無限次元部分多様体幾何 / 幾何学 |
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| Outline of Final Research Achievements |
Main results of this reseach are as follows. First we obtained the homogeneity theorem for ant-Kaehler isoparametric submanfolds in the infnite dimensional anti-Kaehler space under the assumption of a certain kind of diagonalzability of the shape operators and furthermore, completed almost the proof of the homogeneity theorem for certain kind of complex equifocal submanifolds in symmetric spaces of non-compact type by using the result. Secondly we obatined the collapsing theorem for the regularized mean curvature flow starting from horizontally convex invariant hypersurfaces in a Hilbert space. Thirdly we obtained a result about the volume-preserving mean curvature flow starting from tubes of nonconstant radius over certain reflective submanifold in rank one symmetric spaces of non-compact type.
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Report
(5 results)
Research Products
(34 results)
