E.D. Rodionov
Einstein metrics on a class of five-dimensional homogeneous spaces

Comment.Math.Univ.Carolinae 32,2 (1991) 389-393.

Abstract:We prove that there is exactly one homothety class of invariant Einstein metrics in each space $SU(2) \times SU(2) / SO(2)_r (r\in Q, |r|\not =1)$ defined below.

Keywords: homogeneous Riemannian manifolds, Einstein manifolds, Ricci tensor, sectional curvature
AMS Subject Classification: 53C25, 53C30