Non-negative Ricci curvature on closed manifolds under Ricci flow
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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 Kähler manifolds and relate to a question raised by Xiuxiong Chen.References
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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
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 675-685
- MSC (2010): Primary 53C44, 53C55, 53C21
- DOI: https://doi.org/10.1090/S0002-9939-2010-10537-3
- MathSciNet review: 2736347