Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the completeness of gradient Ricci solitons

Author(s): Zhu-Hong Zhang
Journal: Proc. Amer. Math. Soc. 137 (2009), 2755-2759.
MSC (2000): Primary 53C20
Posted: March 18, 2009
MathSciNet review: 2497489
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Abstract | References | Similar articles | Additional information

Abstract: A gradient Ricci soliton is a triple 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 implies that of the vector field $\nabla f$ .

References:

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2.: B. Chow, P. Lu, and L. Ni, Hamilton's Ricci flow, Graduate Studies in Mathematics, Amer. Math. Soc., Providence, RI, 2006.
3.: B. Chow, and D. Knopf, The Ricci Flow: An Introduction, Mathematical Surveys and Monographs, vol. 110, Amer. Math. Soc., Providence, RI, 2004. MR 2061425 (2005e:53101)
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Additional Information:

Zhu-Hong Zhang
Affiliation: Department of Mathematics, Sun Yat-sen University, Guangzhou, People's Republic of China 510275
Email: juhoncheung@sina.com

DOI: 10.1090/S0002-9939-09-09866-9
PII: S 0002-9939(09)09866-9
Keywords: Completeness, gradient Ricci soliton, gradient self-similar solution
Received by editor(s): September 22, 2008,
Received by editor(s) in revised form: December 30, 2008
Posted: March 18, 2009
Additional Notes: The author was supported in part by NSFC 10831008 and NKBRPC 2006CB805905.
Communicated by: Richard A. Wentworth
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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