Projective Ricci flat spherically symmetric Finsler metrics

Abstract

In Finsler geometry, the projective Ricci curvature is an important projective invariant. In this paper, we characterize projective Ricci flat spherically symmetric Finsler metrics. Under a certain condition, we prove that a projective Ricci flat spherically symmetric Finsler metric must be a Douglas metric. Moreover, we construct a class of new nontrivial examples on projective Ricci flat Finsler metrics.