Ricci flow does not preserve positive sectional curvature in dimension four
Differential Geometry
2023-02-23 v1
Abstract
We find examples of cohomogeneity one metrics on and with positive sectional curvature that lose this property when evolved via Ricci flow. These metrics are arbitrarily small perturbations of Grove--Ziller metrics with flat planes that become instantly negatively curved under Ricci flow.
Keywords
Cite
@article{arxiv.2112.13291,
title = {Ricci flow does not preserve positive sectional curvature in dimension four},
author = {Renato G. Bettiol and Anusha M. Krishnan},
journal= {arXiv preprint arXiv:2112.13291},
year = {2023}
}
Comments
LaTeX2e, 18 pages, 2 figures