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Myers’ type theorem with the Bakry–Émery Ricci tensor

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Abstract

In this paper, we prove a new Myers’ type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry–Émery Ricci tensor has a positive lower bound. The result is sharper than previous Myers’ type results. The proof uses the generalized mean curvature comparison applied to the excess function instead of the classical second variation of geodesics.

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Acknowledgements

The author would like to thank anonymous referees for pointing out many expression errors and give many valuable suggestions that helped to improve the presentation of the paper. This work is supported by the NSFC (11671141) and the Natural Science Foundation of Shanghai (17ZR1412800).

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  1. Department of Mathematics, Shanghai Maritime University, 1550 Haigang Avenue, Shanghai, 201306, People’s Republic of China

    Jia-Yong Wu

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  1. Jia-Yong Wu
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Wu, JY. Myers’ type theorem with the Bakry–Émery Ricci tensor. Ann Glob Anal Geom 54, 541–549 (2018). https://doi.org/10.1007/s10455-018-9613-5

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  • DOI: https://doi.org/10.1007/s10455-018-9613-5

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