Rigidity of Busemann convex Finsler metrics

Sergei Ivanov; Alexander Lytchak

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arXiv · 1711.02951

Rigidity of Busemann convex Finsler metrics

Sergei Ivanov·Alexander Lytchak

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Abstract

We prove that a Finsler metric is nonpositively curved in the sense of Busemann if and only if it is affinely equivalent to a Riemannian metric of nonpositive sectional curvature. In other terms, such Finsler metrics are precisely Berwald metrics of nonpositive flag curvature. In particular in dimension 2 every such metric is Riemannian or locally isometric to that of a normed plane. In the course of the proof we obtain new characterizations of Berwald metrics in terms of the so-called linear parallel transport.

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BibTeX RIS

Sergei Ivanov, Alexander Lytchak. 2018-02-11. Rigidity of Busemann convex Finsler metrics. https://arxiv.org/abs/1711.02951

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