Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 2, pp. 339-347 (2017)

Berwald spaces of bounded curvature are Riemannian

Nathaphon Boonnam, Rattanasak Hama and Sorin V. Sabau

Prince of Songkla University, Faculty of Science, KMITL and Tokai University

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.

Keywords: Finsler manifolds, Berwald manifolds, holonomy group, Maximal diameter sphere theorem

Classification (MSC2000): 53C60; 53C22

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