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Annals of Global Analysis and Geometry

, Volume 54, Issue 4, pp 541–549 | Cite as

Myers’ type theorem with the Bakry–Émery Ricci tensor

  • Jia-Yong Wu
Article

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.

Keywords

Bakry–Émery Ricci curvature Ricci soliton Myers’ theorem 

Mathematics Subject Classification

Primary 53C25 Secondary 53C20 53C21 

Notes

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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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiPeople’s Republic of China

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