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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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

Abstract:

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 $\nabla f$.
References
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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: juhoncheung@sina.com
  • 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: https://doi.org/10.1090/S0002-9939-09-09866-9
  • MathSciNet review: 2497489