Renato G. Bettiol — Neckpinchhttps://neckpinch.com/authors/renato-g-bettiol/New arXiv papers by Renato G. Bettiol, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Ricci flow does not preserve positive sectional curvature in dimension fourhttps://neckpinch.com/papers/2112.13291/arxiv:2112.13291Sat, 25 Dec 2021 00:00:00 GMTRenato G. Bettiol, Anusha M. Krishnan — We find examples of cohomogeneity one metrics on S⁴ and ℂ P² 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.Ricci flow4-manifoldsSphere theoremsHomogeneous spaces