On Finsler surfaces that are both Douglas and generalized Berwald

Nina Bartelmess                <meta name=

2020/97/3-4 (8) — DOI: 10.5486/PMD.2020.8784 — pp. 381-391

On Finsler surfaces that are both Douglas and generalized Berwald

Authors: Nina Bartelmess and Julius Lang

Abstract:

We prove that in dimension two, a Finsler metric is Douglas and generalized Berwald if and only if it is Berwald or a Randers metric $\alpha+\beta$, where $\beta$ is closed and is of constant length with respect to $\alpha$.

Keywords: Finsler metric, Berwald metric, Douglas metric, generalized Berwald metric

Mathematics Subject Classification: 53B40, 53C60