# Ricci flow does not preserve positive sectional curvature in dimension four

@inproceedings{Bettiol2021RicciFD, title={Ricci flow does not preserve positive sectional curvature in dimension four}, author={Renato G. Bettiol and Anusha M. Krishnan}, year={2021} }

We find examples of cohomogeneity one metrics on S and CP 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.

## One Citation

### Extremality and rigidity for scalar curvature in dimension four

- Mathematics
- 2022

. Following Gromov, a Riemannian manifold is called area-extremal if any modiﬁcation that increases scalar curvature must decrease the area of some tangent 2-plane. We prove that large classes of…

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