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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Non-negative Ricci curvature on closed manifolds under Ricci flow


Author: Davi Máximo
Journal: Proc. Amer. Math. Soc. 139 (2011), 675-685
MSC (2010): Primary 53C44, 53C55, 53C21
Published electronically: August 25, 2010
MathSciNet review: 2736347
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Abstract: In this short paper we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result Böhm and Wilking have for dimensions twelve and above. Moreover, the manifolds constructed here are manifolds and relate to a question raised by Xiuxiong Chen.


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Additional Information

Davi Máximo
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: maximo@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10537-3
PII: S 0002-9939(2010)10537-3
Keywords: Closed 4-manifolds, Kähler manifolds, Ricci curvature, Ricci flow, Kähler-Ricci flow, invariant curvature conditions.
Received by editor(s): November 10, 2009
Received by editor(s) in revised form: April 13, 2010
Published electronically: August 25, 2010
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2010 American Mathematical Society