Berwald spaces of bounded curvature are Riemannian
Differential Geometry
2018-08-10 v1
Abstract
We prove that Berwald spaces whose flag curvature is nowhere vanishing are in fact Riemannian spaces. This means that any Berwald space with flag curvature bounded below by a positive number must be also Riemannian. This rigidity result shows the importance of non-Riemannian examples when imposing flag curvature bounds on Finsler spaces.
Cite
@article{arxiv.1808.02999,
title = {Berwald spaces of bounded curvature are Riemannian},
author = {Nathaphon Boonnam and Rattanasak Hama and Sorin V. Sabau},
journal= {arXiv preprint arXiv:1808.02999},
year = {2018}
}