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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 2, pp. 339-347 (2017)
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Berwald spaces of bounded curvature are Riemannian

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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

**Full text of the article:**

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FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
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