On the completeness of gradient Ricci solitons

Zhang, Zhu-Hong

doi:10.1090/S0002-9939-09-09866-9

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 $\nabla f$.

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