On the classification of gradient Ricci solitons

Details On the classification of gradient Ricci solitons On the classification of gradient Ricci solitons

2007-12-08

arxiv.org/abs/0712.1298v5

Mathematics

Differential Geometry

14 pages. case. v.4--Added formula for the f-laplacian of the curvature operator and applications

Scientific paper

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.

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