Non-negative Ricci curvature on closed manifolds under Ricci flow
Differential Geometry
2009-12-01 v2 Analysis of PDEs
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 \cite{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, \cite{BW}. Moreover, the manifolds constructed here are \Kahler manifolds and relate to a question raised by Xiuxiong Chen in \cite{XC}, \cite{XCL}.
Cite
@article{arxiv.0911.1827,
title = {Non-negative Ricci curvature on closed manifolds under Ricci flow},
author = {Davi Maximo},
journal= {arXiv preprint arXiv:0911.1827},
year = {2009}
}
Comments
New version with added references and corrected typos