Myers’ type theorem with the Bakry–Émery Ricci tensor

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...

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 54; no. 4; pp. 541 - 549
Main Author Wu, Jia-Yong
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2018
Springer Nature B.V
Subjects
Analysis
Curvature
Differential Geometry
Geodesy
Geometry
Global Analysis and Analysis on Manifolds
Lower bounds
Mathematical Physics
Mathematics
Mathematics and Statistics
Secondary 53C20
Ricci soliton
Myers’ theorem
Bakry–Émery Ricci curvature
Primary 53C25
53C21
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Summary: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.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-018-9613-5