On the classification of gradient Ricci solitons

Peter Petersen, William Wylie

Research output: Contribution to journalArticlepeer-review

108 Scopus citations

Abstract

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
Volume14
Issue number4
DOIs
StatePublished - 2010
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology

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