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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
On the classification of gradient Ricci solitons

Peter Petersen and William Wylie

Geometry & Topology 14 (2010) 2277–2300
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, Sn1 × and n. 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 n, n1 × , n, Sn1 × or Sn.

Keywords
Ricci soliton, Weyl tensor, locally conformally flat, three manifold, constant scalar curvature
Mathematical Subject Classification 2000
Primary: 53C25
References
Publication
Received: 26 June 2008
Accepted: 30 August 2010
Published: 29 October 2010
Proposed: Walter Neumann
Seconded: Tobias Colding, Steven Ferry
Authors
Peter Petersen
Department of Mathematics
University of California, Los Angeles
520 Portola Plaza
Los Angeles CA 90095
USA
http://www.math.ucla.edu/~petersen
William Wylie
Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
209 South 33rd Street
Philadelphia PA 19104
USA
http://www.math.upenn.edu/~wylie