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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 Riemannian manifolds, homogeneous spaces, Einstein metrics, Stiefel manifolds
MSC Classifications: 53C25, 53C30 show english descriptions Special Riemannian manifolds (Einstein, Sasakian, etc.)
Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
 

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