Some Einstein–Randers metrics on homogeneous spaces

Abstract

In this paper we study invariant Einstein–Randers metrics on some homogeneous Riemannian manifolds of rank ≥ 2 . By finding out all the invariant Killing vector fields on the corresponding homogeneous Einstein Riemannian manifolds, we obtain a complete description of all the invariant Einstein–Randers metrics on those homogeneous manifolds. Since the underlying Riemannian Einstein metrics are generically not diagonal, this presents a large number of non-Riemannian homogeneous Einstein–Randers spaces of nonconstant flag curvature.