On conformal transformation of $\boldsymbol m$-th root Finsler metric

B. Tiwari, M. Kumar

The purpose of the present paper is to study the conformal transformation of $m$-th root Finsler metric. The spray coefficients, Riemann curvature and Ricci curvature of conformally transformed $m$-th root metrics are shown to be certain rational functions of direction. Further, under certain conditions it is shown that a conformally transformed $m$-th root metric is locally dually flat if and only if the transformation is a homothety. Moreover the conditions for the transformed metrics to be Einstein and isotropic mean Berwald curvature are also found.