Conformally Flat 4-th root (α, β)-Metrics with Relatively Isotropic Mean Landsberg Curvature

Abstract

In this paper, we study conformally flat 4-th root (α, β)metrics on a manifold M of dimension n ≥ 3. We prove that every conformally flat 4-th root (α, β)-metric with relatively isotropic mean Landsberg curvature must be either Riemannian metrics or locally Minkowski metrics. MSC(2010): 53B40; 53C60.