ON CONFORMALLY FLAT p-POWER (alpha,beta)-METRICS

The purpose of this paper is to study the class of conformally flat p-power (alpha,beta)-metrics F = alpha(1 + beta/alpha)^p, where p ̸= 0 is a constant. This metric is interesting, because for p = -1; 1/2; 1; 2 it reduces to the Matsumoto, square-root, Randers, and square metric, respectively. We prove that if a p-power (alpha,beta)-metric has relatively isotropic mean Landsberg curvature, then it is either a Riemannian metric or a locally Minkowski metric.