2015 Fiscal Year Final Research Report
Einstein metrics on compact homogeneous spaces
| Project/Area Number |
25400071
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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 | Osaka University |
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Principal Investigator |
SAKANE Yusuke 大阪大学, その他部局等, 名誉教授 (00089872)
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| Research Collaborator |
Andreas Arvanitoyeorgos
Ioannis Chrysikos
Marina Statha
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 等質アインシュタイン計量 / 一般化された旗多様体 / Stiefel多様体 / コンパクト単純リー群 / 一般化されたWallach空間 / リッチテンソル / グレブナー基底 |
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| Outline of Final Research Achievements |
We studied invariant Einstein metrics on compact homogeneous spaces. In particular, we found new Einstein metrics on generalized flag manifolds, Stiefel manifolds and compact simple Lie groups.
We determined all generalized flag manifolds with 5 isotropy summands and found all invariant Einstein metrics on these manifolds. Moreover, we constructed new Einstein metrics on Stiefel manifolds and non naturally reductive Einstein metrics on special orthogonal groups SO(n) (n > 6) and symplectic groups Sp(n) ( n > 2).
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| Free Research Field |
幾何学
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