On Landsberg Warped Product Metrics

Abstract

In this paper, we discuss a class of Finsler metrics which are called Finsler warped product metrics. These metrics have been studied by Chen-Shen-Zhao, 2018. Basically, we study the Berwald curvature of Finsler warped product metrics. Also, we characterize the Finsler warped product metrics of isotropic Berwald curvature, then we obtain that they are Randers metrics (Theorem 1.2). Moreover, we consider an important problem which is unicorn problem in Finsler geometry for the class of Finsler metrics. In fact, we get the answer of the crucial question of this study that whether or not such a Landsberg Finsler warped product metric is a Berwald metric (Theorem 1.3).