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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 195–197 | Cite as

An extension of Bonnet–Myers theorem

  • Jianming WanEmail author
Article
  • 158 Downloads

Abstract

We give a complementary generalization of the extensions of Bonnet–Myers theorem obtained by Calabi and also Cheeger–Gromov–Taylor.

Keywords

Bonnet–Myers theorem Ricci curvature Ray 

Mathematics Subject Classification

53C20 53C21 

References

  1. 1.
    Calabi, E.: On Ricci curvature and geodesics. Duke Math. J. 34, 667–676 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
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    Cheeger, J., Gromov, M., Taylor, M.: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differ. Geom. 17(1), 15–53 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
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    Dai, X., Wei, G.: A comparison-estimate of Toponogov type for Ricci curvature. Math. Ann. 303(2), 297–306 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wu, H., Shen, C., Yu, Y.: An Introduction to Riemannian Geometry (in Chinese). Beijing University Press, Beijing (1989)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsNorthwest UniversityXi’anChina

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