On the classification of gradient Ricci solitons
Differential Geometry
2014-11-11 v5
Abstract
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.
Cite
@article{arxiv.0712.1298,
title = {On the classification of gradient Ricci solitons},
author = {Peter Petersen and William Wylie},
journal= {arXiv preprint arXiv:0712.1298},
year = {2014}
}
Comments
14 pages. case. v.4--Added formula for the f-laplacian of the curvature operator and applications