Rigidity of gradient Ricci solitons

Peter Petersen, William Wylie

Research output: Contribution to journalArticlepeer-review

169 Scopus citations


We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×Γ R{double-struck}k where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci solitons are also explained in the last section.

Original languageEnglish (US)
Pages (from-to)329-345
Number of pages17
JournalPacific Journal of Mathematics
Issue number2
StatePublished - Jun 2009
Externally publishedYes


  • Complete manifold
  • Constant scalar curvature
  • Einstein manifold
  • Ricci soliton

ASJC Scopus subject areas

  • General Mathematics


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