On isotropic projective Ricci curvature of C-reducible Finsler metrics

Authors: LAYA GHAEMNEZHAD, BAHMAN REZAEI, MEHRAN GABRANI

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.

Keywords: Isotropic PRic-curvature, C-reducible Finsler metrics, Douglas metric, scalar flag curvature

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