The S-curvature of Finsler warped product metrics

Abstract

The class of warped product metrics can often be interpreted as key space models for general theory of relativity and in the theory of space-time structure. In this paper, we study one of the most important non-Riemannian quantities in Finsler geometry which is called the S-curvature. We examined the behavior of the S-curvature in the Finsler warped product metrics. We are going to prove that every Finsler warped product metric $R\times R^n$ has almost isotropic S-curvature if and only if it is a weakly Berwald metric. Moreover, we show that every Finsler warped product metric has isotropic S-curvature if and only if S-curvature vanishes.