New examples of homogeneous Einstein metrics

A Riemannian metric is said to be Einstein if the Ricci curvature is a constant multiple 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 Riemannian geometry is for the most part unsolved (cf. [Bes]). As a global PDE or a variational problem, the question is intractible. It becomes more manageabl