On D-Recurrent Finsler Metrics

Abstract

In this paper, we study D-recurrent Finsler metrics and characterize D-recurrent Randers metrics. Indeed, we show that a Randers metric $$F=\alpha +\beta $$ is D-recurrent if and only if $$\mathrm{d}\beta $$ is nearly recurrent. We prove that a GDW-Randers metric is a Douglas metric provided that it is D-recurrent. Then, we extend this fact to all the Finsler metrics: GDW-metrics are Douglas metric if they are D-recurrent. Then, we show that in the class of spherically symmetric Finsler metrics, Douglas metrics coincide with D-recurrent ones.