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Existence and non-existence of homogeneous Einstein metrics. (English) Zbl 0596.53040

In this article, the authors prove a general existence theorem for compact homogeneous Einstein metrics, in terms of the size of the isotropy subgroup. As a result they provide many new examples of such metrics. Using geometric arguments, they also exhibit some simply connected homogeneous spaces admitting no homogeneous Einstein metrics. As a corollary, they show that the evolution equation for the Ricci curvature (as modified by R. S. Hamilton), although locally uniquely solvable, may not have global solutions converging to an Einstein metric.
Reviewer: J.P.Bourguignon

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30 Differential geometry of homogeneous manifolds
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References:

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