1. On isotropic projective Ricci curvature of C-reducible Finsler metrics
- Author
-
Laya Ghaemnezhad, Bahman Rezaei, and Mehran Gabrani
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Isotropy ,Scalar (mathematics) ,Curvature ,01 natural sciences ,010101 applied mathematics ,Isotropic PRic-curvature,C-reducible Finsler metrics,Douglas metric,scalar flag curvature ,Mathematics::Metric Geometry ,Projective invariants ,Finsler manifold ,Mathematics::Differential Geometry ,0101 mathematics ,Projective test ,Ricci curvature ,Mathematics - 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.
- Published
- 2019