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# Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

Published:2009-12-01
Printed: Dec 2009
• Andreas Arvanitoyeorgos
• V. V. Dzhepko
• Yu. G. Nikonorov
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## Abstract

A Riemannian manifold $(M,\rho)$ is called Einstein if the metric $\rho$ satisfies the condition \linebreak$\Ric (\rho)=c\cdot \rho$ 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 $\SO(n)/\SO(l)$. 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.
 Keywords: Riemannian manifolds, homogeneous spaces, Einstein metrics, Stiefel manifolds
 MSC Classifications: 53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

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