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A gradient Ricci soliton is a triple ( M , g , f ) (M,g,f) satisfying R i j + ∇ i ∇ j f = λ g i j Rᵢⱼ+∇ _i∇ _j f =λ gᵢⱼ for some real number λ λ . In this paper, we will show that the completeness of the metric g g implies that of the vector field ∇ f ∇ f .
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Zhuhong Zhang (2009) studied this question.
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