Eigenvalue problems on Riemannian manifolds with a modified Ricci tensor |
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| Authors: | Qi-hua Ruan Fan Chen |
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| Affiliation: | 1. Department of Mathematic, Putian University, Putian?, 351100, China
2. School of Mathematic and Statistics, Minnan Normal University, Zhangzhou?, 363000, China
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| Abstract: | In this paper, we study the eigenvalue problems on a Riemannian manifold with a modified Ricci tensor. We obtain some sharp lower bound estimates for the first eigenvalue of Laplacian. We also prove some rigidity theorems for the Riemannian manifold with some suitable conditions. |
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