2013 Fiscal Year Final Research Report
Applications of geometry of symmetric spaces to submanifold theory
| Project/Area Number |
23540108
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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 |
TANAKA Makiko 東京理科大学, 理工学部, 教授 (20255623)
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| Project Period (FY) |
2011 – 2013
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| Keywords | エルミート対称空間 / 実形の交叉 / 対蹠集合 / 対称Ｒ空間 |
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| Research Abstract |
A symmetric space is a Riemannian manifold which admits the geodesic symmetry at each point, which is an important and fundamental object in differential geometry. The principal investigator proved, in the joint work with Hiroyuki Tasaki, that the intersection of two real forms in a Hermitian symmetric space M of compact type is an antipodal set where M is not necessarily irreducible. She also proved, in the joint work with Peter Quast, that any reflective submanifold in a symmetric R-space is convex. And she also proved, in the joint work with Jost-Hinrich Eschenburg and Quast, that any isometry of a semisimple Hermitian symmetric space M can be extended to a linear isometry of the Lie algebra of G when M is realized as an adjoint orbit of a semisimple Lie group G.
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