Invariant Einstein Metrics on Certain Homogeneous Spaces

Projective Invariant Metrics for Einstein Spaces

Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ 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 symplecti...

Some New Homogeneous Einstein Metrics on Symmetric Spaces

We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with rank(M) > 1, not isometric to a compact Lie group. Whenever there exists a closed proper subgroup G of Isom(M) acting transitively on M we nd all G-homogeneous (non-symmetric) Einstein metrics on M .

On invariant domains in certain complex homogeneous spaces

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Homogeneous Einstein metrics on Stiefel manifolds

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.