On compact L-reducible Finsler manifolds

The class of L-reducible Finsler metric was introduced by Matsumoto as a generalization of Randers metrics. One open problems in Finsler Geometry is to find a L-reducible metric which is not of Randers-type. Let  (M,F) be a compact ۳-dimensional L-reducible metric. Suppose that F has constant relatively isotropic mean Landsberg curvature. Then we show that F reduces to a Randers metric.

Keywords:

L-reducible metric , Randers metric , Landsberg metric