On isotropic projective Ricci curvature of C-reducible Finsler metrics

Abstract

Projective Ricci curvature is a projective invariant quantity in Finsler geometry which is introduced by Z. Shen. In this paper, we study special projective Ricci curvature of C-reducible Finsler metrics. The necessary and sufficient conditions of these metrics, which cause these metrics to be weak or isotropic projective Ricci curvature, are found and it is proved that C-reducible Douglas metric of isotropic PRic-curvature must be PRic flat. The same theorem for C-reducible metrics of scalar flag curvature is also investigated.