On projective invariants of general spherically symmetric Finsler spaces in Rn

Abstract

In this paper we discuss projective invariants of general spherically symmetric Finsler metrics in R-n. We obtain the necessary and sufficient conditions for the metrics to be projectively Ricci flat, Weyl and W-quadratic types. In particular, we use the spray theory to give a short proof of the well-known theorem, that is, Finsler manifold is of scalar flag curvature if and only if F is Weyl metric . Therefore, considering the technique of the proof, we obtain a necessary and sufficient condition for the metrics of scalar flag curvature to be Weyl metric. Also, under a certain condition, we prove that projectively Ricci flat general spherically symmetric metrics coincide with the Douglas type metric.(c) 2022 Elsevier B.V. All rights reserved.