On the classification of gradient Ricci solitons

Peter Petersen, William Wylie

Research output: Contribution to journalArticlepeer-review

133 Scopus citations


We show that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci tensor satisfying a weak integral condition are quotients of the standard ones Sn, Sn-1 R and Rn . This gives a new proof of the Hamilton–Ivey–Perelman classification of 3–dimensional shrinking gradient solitons. We also show that gradient solitons with constant scalar curvature and suitably decaying Weyl tensor when noncompact are quotients of Hn, Hn 1 R, Rn, Sn-1 R or Sn .

Original languageEnglish (US)
Pages (from-to)2277-2300
Number of pages24
JournalGeometry and Topology
Issue number4
StatePublished - 2010
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


Dive into the research topics of 'On the classification of gradient Ricci solitons'. Together they form a unique fingerprint.

Cite this