Invariant Einstein metrics on some homogeneous spaces of classical Lie groups

الأصل · EN

A Riemannian manifold (M,ρ) is called Einstein if the metric ρ satisfies the condition (ρ)=c· ρ 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), and on the symplectic analogues Sp(n)/Sp(l). Furthermore, we show that for any positive integer p there exists a Stiefel manifold SO(n)/SO(l) and a homogenous space Sp(n)/Sp(l) which admit at least p SO(n) (resp. Sp(n))-invariant Einstein metrics.