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Gap results for compact quasi-Einstein metrics

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Abstract

In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison theorem for the weighted heat kernel. In the second part, we establish two gap results for the Ricci curvature and the scalar curvature, based on which some rigid properties can be derived.

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Acknowledgements

This work was supported by Natural Science Foundation of Jiangsu Province (Grant No. BK20141235).

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Authors and Affiliations

  1. School of Science, Nantong University, Nantong, 226007, China

    Linfeng Wang

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  1. Linfeng Wang
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Correspondence to Linfeng Wang.

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Wang, L. Gap results for compact quasi-Einstein metrics. Sci. China Math. 61, 943–954 (2018). https://doi.org/10.1007/s11425-016-9049-9

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  • DOI: https://doi.org/10.1007/s11425-016-9049-9

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