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On the completeness of gradient Ricci solitons
Zhu-Hong Zhang
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Source: Crossref
Published: Mar 18, 2009
DOI: 10.1090/s0002-9939-09-09866-9
Open original source ↗Source abstract
A gradient Ricci soliton is a triple ( M , g , f ) (M,g,f) satisfying R i j + ∇ i ∇ j f = λ g i j R_{ij}+\nabla _i\nabla _j f =\lambda g_{ij} for some real number λ \lambda . In this paper, we will show that the completeness of the metric g g implies that of the vector field ∇ f \nabla f .
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