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.
Isotropic PRic-curvature, C-reducible Finsler metrics, Douglas metric, scalar flag curvature
GHAEMNEZHAD, LAYA; REZAEI, BAHMAN; and GABRANI, MEHRAN
"On isotropic projective Ricci curvature of C-reducible Finsler metrics,"
Turkish Journal of Mathematics: Vol. 43:
3, Article 46.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/46