On rotationally invariant shrinking Ricci solitons

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimensions n ≥ 3 and prove that the only complete metrics on Sn, Rn, and R × Sn-1 that admit shrinking soliton structures are respectively the round, flat, and standard cylindrical metrics.

Original languageEnglish (US)
Pages (from-to)73-88
Number of pages16
JournalPacific Journal of Mathematics
Volume236
Issue number1
DOIs
StatePublished - May 2008
Externally publishedYes

Fingerprint

Ricci Soliton
Shrinking
Metric
Soliton Equation
Invariant
Solitons
Gradient
Standards

Keywords

  • Ricci flow
  • Ricci solitons

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On rotationally invariant shrinking Ricci solitons. / Kotschwar, Brett.

In: Pacific Journal of Mathematics, Vol. 236, No. 1, 05.2008, p. 73-88.

Research output: Contribution to journalArticle

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