On the Completeness of Gradient Ricci Solitons

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 $\nabla f$.

5 pages

Cited by in corpus (1)

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