On rotationally invariant shrinking Ricci solitons

Brett Kotschwar

doi:10.2140/pjm.2008.236.73

On rotationally invariant shrinking Ricci solitons

Brett Kotschwar

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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 × S^n-1 that admit shrinking soliton structures are respectively the round, flat, and standard cylindrical metrics.

Original language	English (US)
Pages (from-to)	73-88
Number of pages	16
Journal	Pacific Journal of Mathematics
Volume	236
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2008.236.73
State	Published - May 2008
Externally published	Yes

Keywords

Ricci flow
Ricci solitons

ASJC Scopus subject areas

Mathematics(all)

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10.2140/pjm.2008.236.73

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title = "On rotationally invariant shrinking Ricci solitons",

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.",

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author = "Brett Kotschwar",

year = "2008",

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KW - Ricci flow

KW - Ricci solitons

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On rotationally invariant shrinking Ricci solitons

Abstract

Keywords

ASJC Scopus subject areas

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