On D-Recurrent Finsler Metrics

In this paper, we study D-recurrent Finsler metrics and characterize D-recurrent Randers metrics. Indeed, we show that a Randers metric F = α + β is D-recurrent if and only if dβ 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.