On Finsler warped product metrics with vanishing $E$-curvature

Abstract

In this paper, we study Finsler warped product metric recently introduced 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.

Keywords

• finsler metrics
• warped product
• $e$-curvature
• projectively flat