On Invariant Matsumoto Metrics

Abstract

In this paper, we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces. We first study the intersection between automorphism and isometry groups of these spaces. Then, we study geodesic vectors and investigate the set of all homogeneous geodesics on homogeneous spaces and nilpotent Lie groups of dimension five.