Abstract

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.

Keywords: Finsler space; $m$-th root metric; conformal transformation; locally dually flat metric; Einstein metric; Ricci curvature; isotropic mean Berwald curvature.

MSC: 53B40, 53C60

Pages:  138--145     

Volume  72 ,  Issue  2 ,  2020