A Schur type lemma for the Mean Berwald curvature in Finsler geometry

Ming Li

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arXiv · 2207.12896

A Schur type lemma for the Mean Berwald curvature in Finsler geometry

Ming Li

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Abstract

In this short paper, we study a symmetric covariant tensor in Finsler geometry, which is called the mean Berwald curvature. We first investigate the geometry of the fibres as the submanifolds of the tangent sphere bundle on a Finsler manifold. Then we prove that if the mean Berwald curvature is isotropic along fibres, then the Berwald scalar curvature is constant along fibres.

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Ming Li. 2022-07-26. A Schur type lemma for the Mean Berwald curvature in Finsler geometry. https://arxiv.org/abs/2207.12896

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