On Finsler Warped Product Metrics with Special Curvatures Properties

Abstract

In this paper, we study a class of Finsler metrics called Finsler warped product metrics. We prove that every Finsler warped product metric is of isotropic E-curvature if and only if it is of isotropic S-curvature. Moreover, we prove that if the metric is of Douglas type and has isotropic S-curvature, then it must be Randers metric or Berwald metric.