On L-reducible Finsler manifolds

Document Type : Original Article


School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846 -13114, Iran E-mail: h beizavi@mathdep.iust.ac.ir


In this paper, we consider the class of L-reducible Finsler metrics which contains the class of C-reducible metrics and the class of Landsberg metrics. Let (M,F) be a 3-dimensional L-reducible Finsler manifold. Suppose that F has a relatively isotropic mean Landsberg curvature. We find a condition on the main scalars of F under which it reduces to a Randers metric or a Landsberg metric.