Finsler surfaces with vanishing T-tensor

Abstract

In this paper, for Finsler surfaces, we prove that the T-condition and σT-condition coincide. For higher dimensions n≥3, we illustrate by an example that the T-condition and σT-condition are not equivalent. We show that the non-homothetic conformal change of a Berwald (resp. a Landsberg) surface is Berwaldian (resp. Landsbergian) if and only if the σT-condition is satisfied. By solving the Landsberg's PDE, we classify all Finsler surfaces satisfying the T-condition, or equivalently the σT-condition. Some examples are provided and studied.