Cohomogeneity One Randers Metrics

Abstract

AbstractAn action of a Lie group G on a smooth manifold M is called cohomogeneity one if the orbit space M/G is of dimension 1. A Finsler metric F on M is called invariant if F is invariant under the action of G. In this paper, we study invariant Randers metrics on cohomogeneity one manifolds. We first give a sufficient and necessary condition for the existence of invariant Randers metrics on cohomogeneity one manifolds. Then we obtain some results on invariant Killing vector fields on the cohomogeneity one manifolds and use them to deduce some sufficient and necessary conditions for a cohomogeneity one Randers metric to be Einstein.