A Schur type lemma for the mean Berwald curvature in Finsler geometry |
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Institution: | Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, PR China |
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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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Keywords: | Berwald curvature Berwald scalar curvature |
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