On Riemann curvature of spherically symmetric metrics

Abstract

In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct a Berwald frame for a spherically symmetric Finsler surface and calculate some associated geometric objects. Several examples are provided and discussed. Finally, we give a note on a certain general $(\alpha,\beta)$-metric that appears in the literature.