Locally dually flatness and locally projectively flatness of Matsumoto change with m-th root Finsler metrics

In this paper, we study the Matsumoto change of m-th root Finsler metric. We find the necessary and sufficient conditions under which the transformed metric be locally dually flat. Also, we prove that for Matsumoto change of m-th root metric is locally projectively flat if and only if it is locally Minkowskian.

Keywords:

Finsler metric , m-th root metric , Matsumoto change , Locally projectively flat metric and Locally dually flat metric