On the Ricci curvature of a Randers metric of isotropic <Emphasis Type="Italic">S</Emphasis>-curvature |
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Authors: | Xiao Huan Mo Chang Tao Yu |
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Institution: | (1) Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China |
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Abstract: | We derive the integral inequality of a Randers metric with isotropic S-curvature in terms of its navigation representation. Using the obtained inequality we give some rigidity results under the
condition of Ricci curvature. In particular, we show the following result: Assume that an n-dimensional compact Randers manifold (M, F) has constant S-curvature c. Then (M, F) must be Riemannian if its Ricci curvature satisfies that Ric < −(n − 1)c
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This work is supported by the National Natural Science Foundation of China (10471001) |
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Keywords: | Finsler manifold Randers metric Ricci curvature |
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