On the special $(\alpha, \beta)$-change of a Finsler space with $m$-th root metric

Abstract

The present paper focuses on the theory of transformation of the $m$-th root metric. We find that the transformed $m$-th root metric and the $m$-th root metric are projectively related. Further, we establish a necessary and sufficient condition for a transformed $m$-th root metric to be locally dually flat and projectively flat.