Invariant (α, β)-metrics on homogeneous manifolds

Abstract

In this paper we study invariant (α, β)-metrics on homogeneous spaces. We first give a method to construct invariant (α, β)-metrics on homogeneous spaces. Then we obtain some conditions for some special type of (α, β)-metrics to be of Berwald type and Douglas type. At last, we give a rigidity result concerning the Randers metrics and Matsumoto metrics of Berwald type on homogeneous spaces.