Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

A Riemannian manifold (M, rho) is called Einstein if the metric rho satisfies the condition Ric(rho) = c . rho for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics, with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l). Furthermore, we show that for any positive integer p there exists a Stiefel manifold SO(n)/SO(l) that admits at least p SO(n)-invariant Einstein metrics.