On L-reducible Finsler manifolds

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 ۳-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.

Keywords:

L-reducible Finsler metric , C-reducible metric , Randers metric , Landsberg metric