On Homogeneous Randers Metrics

Abstract

In this paper, we study the curvature features of the class of homogeneous Randers metrics. For these metrics, we first find a reduction criterion to be a Berwald metric based on a mild restriction on their Ricci tensors. Then, we prove that every homogeneous Randers metric with relatively isotropic (or weak) Landsberg curvature must be Riemannian. This provides an extension of well-known Deng-Hu theorem that proves the same result for a homogeneous Berwald-Randers metric of non-zero flag curvature.