On generalized ۴-th root Finsler metrics

In this paper, we prove that every generalized cubic Finsler metric with vanishing Landsberg curvature is a Berwald metric. This yields an extension of Matsumoto theorem for the cubic metric. Then, we show that every generalized ۴-th root Finsler metric with vanishing Landsberg curvature is a Berwald metric.

Keywords:

۴-th root metrics , cubic metric , Landsberg metric , Berwald metric