Non-negative Ricci curvature on closed manifolds under Ricci flow

Abstract

In this short note 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 in K for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result B\"ohm and Wilking have for dimensions twelve and above, BW. Moreover, the manifolds constructed here are manifolds and relate to a question raised by Xiuxiong Chen in XC, XCL.

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