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| A Class of Homogeneous Einstein Manifolds |
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Citation： |
Yifang KANG,Ke LIANG.A Class of Homogeneous Einstein Manifolds[J].Chinese Annals of Mathematics B,2006,27(4):411~418 |
| Page view： 1089
Net amount： 1078 |
Authors： |
Yifang KANG; Ke LIANG |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10431040, No.10501025) and
the Liu Hui Center for Applied Mathematics. |
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| Abstract： |
A Riemannian manifold $(M,g)$ is called Einstein manifold if its
Ricci tensor satisfies $r=c\cdot g$ for some constant $c$. General
existence results are hard to obtain, e.g., it is as yet unknown
whether every compact manifold admits an Einstein metric. A
natural approach is to impose additional homogeneous assumptions.
M. Y. Wang and W. Ziller have got some results on compact
homogeneous space $G/H$. They investigate standard homogeneous
metrics, the metric induced by Killing form on $G/H$, and get some
classification results. In this paper some more general
homogeneous metrics on some homogeneous space $G/H$ are studies,
and a necessary and sufficient condition for this metric to be
Einstein is given. The authors also give some examples of Einstein
manifolds with non-standard homogeneous metrics. |
Keywords： |
Einstein manifold, Homogeneous space, General homogeneous metric |
Classification： |
53C25, 53C30 |
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