Invariant naturally reductive Randers metrics on homogeneous spaces

Purpose: The purpose of this paper is to study the geometric properties of naturally reductive homogeneous Randers spaces.Methods: We use Lie theory methods in the study of Finsler geometry.Results: We first prove that if a Randers metric is naturally reductive, then the underlying Riemannian metric is naturally reductive. Then, we show that, for Berwald type Randers metric, if the underlying Riemannian metric is naturally reductive, then the Randers metric is naturally reductive. Finally, we give a geometric criterion of homogeneous naturally reductive Randers spaces.Conclusions: This paper provides a convenient method to construct naturally reductive Randers metrics on homogeneous Riemannian manifolds.