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On the completeness of gradient Ricci solitons

Author: Zhu-Hong Zhang
Journal: Proc. Amer. Math. Soc. 137 (2009), 2755-2759
MSC (2000): Primary 53C20
Published electronically: March 18, 2009
MathSciNet review: 2497489
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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 [Enhancements On Off] (What's this?)

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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

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
Published electronically: March 18, 2009
Additional Notes: The author was supported in part by NSFC 10831008 and NKBRPC 2006CB805905.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.