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Corpus ID: 203836098

Finsler metrics that are both Douglas and generalized Berwald in dimension two

@article{Bartelmess2019FinslerMT,
title={Finsler metrics that are both Douglas and generalized Berwald in dimension two},
author={Nina Bartelmess and Julius Lang},
journal={arXiv: Differential Geometry},
year={2019}
}

We proof 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 $\alpha$.

Riemannian metrics are special Berwald metrics. In fact, Berwald metrics are “almost Riemannian” in the sense that every Berwald metric is affinely equivalent to a Riemannian metric, i.e., the… Expand

In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We find an equation that characterizes Douglas metrics on a manifold of dimension n ≧ 3.

We correct a mistake in Shen Yibing, Yu Yaoyong, On Projectively Related Randers Metrics, International Journal of Mathematics 19}(2008), no. 5, 503--520, and prove the natural generalization of the… Expand

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… Expand

In this paper, we study Zermelo navigation on Riemannian manifolds and use that to solve a long standing problem in Finsler geometry, namely the complete classification of strongly convex Randers… Expand