On the Completeness of Gradient Ricci Solitons

Details On the Completeness of Gradient Ricci Solitons On the Completeness of Gradient Ricci Solitons

2008-07-10

arxiv.org/abs/0807.1581v3

Mathematics

Differential Geometry

5 pages

Scientific paper

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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