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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On locally conformally flat gradient steady Ricci solitons


Authors: Huai-Dong Cao and Qiang Chen
Journal: Trans. Amer. Math. Soc. 364 (2012), 2377-2391
MSC (2010): Primary 53C21, 53C25
Published electronically: December 13, 2011
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Abstract: In this paper, we classify $ n$-dimensional ($ n\geq 3$) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact nonflat locally conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.


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Additional Information

Huai-Dong Cao
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email: huc2@lehigh.edu

Qiang Chen
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email: qic208@lehigh.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05446-2
PII: S 0002-9947(2011)05446-2
Received by editor(s): March 9, 2010
Received by editor(s) in revised form: March 15, 2010
Published electronically: December 13, 2011
Additional Notes: The first author was partially supported by NSF Grants DMS-0506084 and DMS-0909581.
The second author was partially supported by NSF Grant DMS-0354621 and a Dean’s Fellowship of the School of Arts and Sciences at Lehigh University.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.