Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups
نویسنده
چکیده
A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(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. 2000 Mathematical Subject Classification: 53C25, 53C30.
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