New Examples of Homogeneous Einstein Metrics

摘要

A Riemannian metric is said to be Einstein if the Ricci curvature is a constant mul- tiple of the metric. Given a manifold M, one can ask whether M carries an Einstein metric and, if so, how many. This fundamental question in Rimannian geometry is for the most part unsolved (cf. [Bes]). As a global PDE or a variational problem, the question is intractible. It becomes more manageable in the homogeneous set- ting, and so many of the known examples of compact simply connected Einstein manifolds are homogeneous.