ON CONFORMALLY FLAT p-POWER (alpha,beta)-METRICS
Abstract
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.
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DOI: https://doi.org/10.22190/FUMI240228013Z
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