On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach

Abstract

Abstract In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Lands-berg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner’s original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.