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

Csaba Vincze 1 , Tahere Reza Khoshdani 2 , Sareh Mehdi Zadeh Gilani 3 , and Márk Oláh 4
  • 1 Institute of Mathematics, University of Debrecen, H-4002, Debrecen, Hungary
  • 2 Institute of Mathematics, University of Debrecen, H-4002, Debrecen, Hungary
  • 3 Institute of Mathematics, University of Debrecen, H-4002, Debrecen, Hungary
  • 4 Institute of Mathematics, University of Debrecen, H-4002, Debrecen, Hungary

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.

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