Invariant Einstein metrics on some homogeneous spaces of classical Lie groups

Details Invariant Einstein metrics on some homogeneous spaces of classical Lie groups Invariant Einstein metrics on some homogeneous spaces of classical Lie groups

2006-12-18

arxiv.org/abs/math/0612504v2

Mathematics

Differential Geometry

Scientific paper

A Riemannian manifold $(M,\rho)$ is called Einstein if the metric $\rho$ satisfies the condition $\Ric (\rho)=c\cdot \rho$ 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 $SO(n)/SO(l)$, 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.

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