Some New Homogeneous Einstein Metrics on Symmetric Spaces

Abstract

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