2011 Fiscal Year Final Research Report
Homogeneous Einstein manifolds
| Project/Area Number |
21540080
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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 | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAMARU Hiroshi 広島大学, 大学院・理学研究科, 准教授 (50306982)
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 | 等質アインシュタイン計量 / 一般化された旗多様体 / リー群上の左不変リーマン計量 / アインシュタイン可解多様体 / 擬ケーラー計量 / コンパクトリー群上のアインシュタイン計量 |
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| Research Abstract |
For generalized flag manifolds, we completely classified homogeneous Einstein metrics in case that these have four isotropy summands. Moreover, in the cases when generalized flag manifolds have five or six isotropy summands, we obtain the existence of non-Kahler Einstein metrics on these spaces. For solvable Lie groups which are obtained by the extensions of nilpotent Lie subgroups corresponding to the parabolic Lie subalgebras of garaded semi-simple Lie groups, we have proved that there exist always Einstein metrics. We also constructed many compact pseudo-Kahler solvmanifolds with flat Ricci tensor.
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Research Products
(21 results)
