Remarks on generalized m-th root metrics

In this paper, we prove that every generalized m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every generalized m-th root metric with almost vanishing H-curvature has vanishing H-curvature. As well as, we will express a necessary and sufficient condition for the metrics F = √ that is locally projectively flat and locally dually flat. Further, we will express a necessary and sufficient condition for the metric ̃ √ C that be projectively flat. Finally, Randers and conformal -changes of the more generalized m-th root metrics are inspected, when m is odd number.

Remarks on generalized m-th root metrics Keywords:

generalized m-th root metric , Randers change , conformal change , H-curvature , Landsberg metric