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15 April 2013 On Bach-flat gradient shrinking Ricci solitons
Huai-Dong Cao, Qiang Chen
Duke Math. J. 162(6): 1149-1169 (15 April 2013). DOI: 10.1215/00127094-2147649

Abstract

In this article, we classify n-dimensional (n4) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat and hence a finite quotient of the Gaussian shrinking soliton R4 or the round cylinder S3×R. More generally, for n5, a Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Gaussian shrinking soliton Rn or the product Nn1×R, where Nn1 is Einstein.

Citation

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Huai-Dong Cao. Qiang Chen. "On Bach-flat gradient shrinking Ricci solitons." Duke Math. J. 162 (6) 1149 - 1169, 15 April 2013. https://doi.org/10.1215/00127094-2147649

Information

Published: 15 April 2013
First available in Project Euclid: 22 April 2013

zbMATH: 1277.53036
MathSciNet: MR3053567
Digital Object Identifier: 10.1215/00127094-2147649

Subjects:
Primary: 53C21
Secondary: 53C20, 53C25, 53C44

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 6 • 15 April 2013
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