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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the completeness of gradient Ricci solitons
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by Zhu-Hong Zhang PDF
Proc. Amer. Math. Soc. 137 (2009), 2755-2759 Request permission


A gradient Ricci soliton is a triple $(M,g,f)$ satisfying $R_{ij}+\nabla _i\nabla _j f =\lambda g_{ij}$ for some real number $\lambda$. In this paper, we will show that the completeness of the metric $g$ implies that of the vector field $\nabla f$.
  • Shigetoshi Bando, On the classification of three-dimensional compact Kaehler manifolds of nonnegative bisectional curvature, J. Differential Geom. 19 (1984), no. 2, 283–297. MR 755227
  • B. Chow, P. Lu, and L. Ni, Hamilton’s Ricci flow, Graduate Studies in Mathematics, Amer. Math. Soc., Providence, RI, 2006.
  • Bennett Chow and Dan Knopf, The Ricci flow: an introduction, Mathematical Surveys and Monographs, vol. 110, American Mathematical Society, Providence, RI, 2004. MR 2061425, DOI 10.1090/surv/110
  • R. Schoen and S.-T. Yau, Lectures on differential geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, I, International Press, Cambridge, MA, 1994. Lecture notes prepared by Wei Yue Ding, Kung Ching Chang [Gong Qing Zhang], Jia Qing Zhong and Yi Chao Xu; Translated from the Chinese by Ding and S. Y. Cheng; With a preface translated from the Chinese by Kaising Tso. MR 1333601
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Additional Information
  • Zhu-Hong Zhang
  • Affiliation: Department of Mathematics, Sun Yat-sen University, Guangzhou, People’s Republic of China 510275
  • MR Author ID: 868125
  • Email:
  • Received by editor(s): September 22, 2008
  • Received by editor(s) in revised form: December 30, 2008
  • Published electronically: March 18, 2009
  • Additional Notes: The author was supported in part by NSFC 10831008 and NKBRPC 2006CB805905.
  • Communicated by: Richard A. Wentworth
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2755-2759
  • MSC (2000): Primary 53C20
  • DOI:
  • MathSciNet review: 2497489