On projective invariants of general spherically symmetric Finsler spaces in [formula omitted

Abstract

In this paper we discuss projective invariants of general spherically symmetric Finsler metrics in Rn. 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.