Ricci flow does not preserve positive sectional curvature in dimension four

Published 25 Dec 2021 in math.DG | (2112.13291v1)

Abstract: We find examples of cohomogeneity one metrics on $S^4$ and $\mathbb C P^2$ 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.

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