Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups
Printed: Dec 2009
V. V. Dzhepko
Yu. G. Nikonorov
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.
Riemannian manifolds, homogeneous spaces, Einstein metrics, Stiefel manifolds
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]