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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