The purpose of this paper is to study the class of conformally flat p-power (α, β)-metrics F = α(1 + β/α)^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 (α, β)-metric has relatively isotropic mean Landsberg curvature, then it is either a Riemannian metric or a locally Minkowski metric.
