We prove that a Finsler metric has Busemann curvature bounded above (below, respectively) by κ if and only if it is the Berwald metric with flag curvature bounded above (below, respectively) by κ. Combining this with Szabó’s Berwald metrization theorem, we can obtain that such a Finsler metric is affinely equivalent to a Riemannian metric with sectional curvature bounded above (below, respectively) by κ.

Finsler metric, Busemann curvature, Berwald metric.

Received: July 13, 2023; Revised: August 25, 2023; Accepted: September 1, 2023; Published: October 12, 2023

How to cite this article: Chang-Wan Kim, Finsler metrics with Busemann curvature bounds, Far East Journal of Applied Mathematics 116(3) (2023), 249-262. http://dx.doi.org/10.17654/0972096023014

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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