We show that the only complete shrinking gradient Ricci solitons with vanishing Weyl tensor are quotients of the standard ones. This gives a new proof of the Hamilton-Ivey-Perel'man classification of 3-dimensional shrinking gradient solitons. We also prove a classification for expanding gradient Ricci solitons with constant scalar curvature and suitably decaying Weyl tensor.
Petersen, Peter and Wylie, William, "On the Classification of Gradient Ricci Solitons" (2008). Mathematics Faculty Scholarship. 129.
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