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

Document Type : Original Article


1 Department of Mathematics and Computer Science, Victoriei 76 North University, Center of Baia Mare, Technical University of Cluj Napoca, 430122 Baia Mare, Romania. Laurian.PISCORAN@mi.utcluj.ro

2 Department of Mathematics, Faculty of science, University of Qom, Iran. marzeia.amini@gmail.com


Let F = √α(α + β) be a conformally flat square-root (α; β)-metric on a manifold M of dimension n ≥ 3, where α = √aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form on M. Suppose that F has relatively isotropic mean Landsberg curvature. We show that F reduces to a Riemannian
metric or a locally Minkowski metric.