On Finsler warped product metrics with vanishing E-curvature

Abstract

In this paper, we study Finsler warped product metric recently in-troduced by P. Marcal and Z. Shen and find characteristics differential equations for this metric to have vanishing E-curvature. We also prove that if this warped product Finsler metric is projectively flat, then it becomes a Riemannian metric. © 2021, Amirkabir University of Technology. All rights reserved.