Non-negative Ricci curvature on closed manifolds under Ricci flow

Máximo, Davi

doi:10.1090/S0002-9939-2010-10537-3

Non-negative Ricci curvature on closed manifolds under Ricci flow
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Proc. Amer. Math. Soc. 139 (2011), 675-685 Request permission

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.

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