A Class of Homogeneous Einstein Manifolds*
Yifang Kang , Ke Liang
Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (4) : 411 -418.
A Class of Homogeneous Einstein Manifolds*
A Riemannian manifold (M, g) is called Einstein manifold if its Ricci tensor satisfies r = c ⋅ 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.
Einstein manifold / Homogeneous space / General homogeneous metric / 53C25 / 53C30
| [1] |
Besse, A., Einstein Manifolds, Springer Verlag, 1987. |
| [2] |
Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978. |
| [3] |
Humphreys, J. E., Introduction to Lie Algebras and Representation Theory, Springer Verlag, 1972. |
| [4] |
Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry II, Wiley (Interscience), 1969. |
| [5] |
|
| [6] |
|
/
| 〈 |
|
〉 |
PDF
