$SO(N)$-INVARIANT EINSTEIN METRICS ON STIEFEL MANIFOLDS

Andreas Arvanitoyeorgos

1991 Math. Subject Classification: 53C25, 53C30.

Key words: Homogeneous spaces, Einstein metrics, Stiefel manifolds.

Abstract: A Stiefel manifold $V_k\R^n$ is the set of orthonormal
$k$-frames in $\R^n$, and it is diffeomorphic to the homogeneous
space $SO(n)/SO(n-k)$.  We study $SO(n)$-invariant Einstein metrics on this
space by using the variational approach.
We determine when the standard metric on $SO(n)/SO(n-k)$ is Einstein,
 and we give an explicit solution for the space $V_2\R^n$.