English

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.

Keywords

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

R2 v1 2026-06-21T09:52:03.065Z