On conformally flat square-root (α,β)-metrics

Let F = √α(α + β) be a conformally flat square-root (α; β)-metric on a manifold M of dimension n ≥ ۳, where α = √aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a ۱-form on M. Suppose that F has relatively isotropic mean Landsberg curvature. We show that F reduces to a Riemannianmetric or a locally Minkowski metric.

Keywords:

square-root metric , (α , β)-metric , Conformally flat metric , relatively isotropic mean Landsberg curvature