S-curvature of cohomogeneity one Randers spaces

Abstract

In this paper, we study S-curvature of cohomogeneity one Randers spaces with orbit space S1. In particular, we present an explicit coordinate-free formula of S-curvature in terms of some quantities which is determined by the metric and the structure of the manifold. As an application, we give a sufficient and necessary condition for a cohomogeneity one Randers space to have almost isotropy S-curvature. Furthermore, we give some simple criterions for a cohomogeneity one Randers space to be a Berwald space or a Douglas space.