On a new geometrical derivation of two-dimensional Finsler manifolds with constant main scalar

Abstract

In this paper we investigate the problem (it what kind of (two-dimensional) Finsler manifolds have a conformal change leaving the mixed curvature of the Berwald connection invariant?) We establish a differential equation for such Finslerian energy functions and present the solutions under some simplification. As we shall see they are essentially the same as the singular Finsler metrics with constant main scalar determined by L. Berwald.