Conformal Analysis of Generalized Kropina Changes with m-th Root Finsler Metrics

The purpose of the present work is to study the geometric characteristics of m-th root Finsler metrics under a conformal generalized Kropina transformation. We derive expressions for the fundamental tensor and the spray coefficients of the transformed metrics, and demonstrate that these geometric quantities become rational functions in the directional arguments under the conformal transformation. Further, we study the necessary and sufficient conditions for the conformal generalized Kropina transformation of an m-th root metric to be locally dually flat and derive conditions under which the conformal factor is a homothety. Additionally, we provide conditions under which the transformed metric is Einstein.