2011 Fiscal Year Final Research Report
Geometry of Lagrange submanifolds and Ricci solitons
| Project/Area Number |
21540083
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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 | Shimane University |
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Principal Investigator |
KIMURA Makoto 島根大学, 総合理工学部, 教授 (30186332)
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| Co-Investigator(Kenkyū-buntansha) |
FURUMOCHI Tetsuo 島根大学, 総合理工学部, 教授 (40039128)
HATTORI Yasunao 島根大学, 総合理工学部, 教授 (20144553)
YAMADA Takumi 島根大学, 総合理工学部, 講師 (40403117)
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| Project Period (FY) |
2009 – 2011
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| Keywords | リッチ・ソリトン / ラグランジュ部分多様体 |
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| Research Abstract |
We investigated Ricci solitons from the view point of hypersurface geometry.
In particular, we studied locally conformally flat hypersurfaces in space forms such that
The induced metric is a Ricci soliton and the potential vector field is a principal curvature vector of the principal curvature vector of multiplicity one. Then we showed that in the case when the ambient space is Euclidean space, such hypersurface is rotationally invariant.
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