Existence and non-existence of homogeneous Einstein metrics (Q1078825)

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.