Some properties of m-th root Finsler metrics

Abstract

We prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal β-change of anm-th root metric is locally dually flat. Finally, we prove that the conformal β-change of locally projectively flat m-th root metrics are locally Minkowskian.