Finsler conformal transformations and the curvature invariances

Abstract

This article studies the global conformal transformations f on a Finsler space (M, F ), which satisfy f * F = e c(x) F , where F := F (x, y) is a Finsler metric on M and x M , y T x M \ {0}. We obtain the relations between some important geometric quantities of F and their correspondences respectively, including Riemann curvatures, Ricci curvatures, Landsberg curvatures, mean Landsberg curvatures and S-curvatures. Then, we discuss the properties of those conformal transformations on (M