# Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature

@article{Bettiol2019FourdimensionalCO, title={Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature}, author={Renato G. Bettiol and Anusha M. Krishnan}, journal={Communications in Analysis and Geometry}, year={2019} }

We exhibit the first examples of closed 4-manifolds with nonnegative sectional curvature that lose this property when evolved via Ricci flow.

## 11 Citations

Ricci flow does not preserve positive sectional curvature in dimension four

- Mathematics
- 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…

Convergence of Ricci flow solutions to Taub-NUT

- Mathematics
- 2021

Abstract We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric g 0 on with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If g 0 has bounded…

On the stability of harmonic maps under the homogeneous Ricci flow

- MathematicsComplex Manifolds
- 2018

Abstract In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow.We provide examples where the stability (non-stability) is preserved under…

Ricci Flow On Cohomogeneity One Manifolds

- Mathematics
- 2019

RICCI FLOW ON COHOMOGENEITY ONE MANIFOLDS Anusha Mangala Krishnan Wolfgang Ziller In the first part of this thesis, in joint work with Renato Bettiol, we show that the geometric property of…

Diagonalizing the Ricci Tensor

- MathematicsThe Journal of Geometric Analysis
- 2020

We show that a basis of a semisimple Lie algebra for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being ``nice''. Namely,…

Convergence of Ricci flow solutions to Taub-NUT

- Mathematics
- 2020

We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric $g_{0}$ on $\mathbb{R}^{4}$ with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If…

Global bifurcation techniques for Yamabe type equations on Riemannian manifolds

- MathematicsNonlinear Analysis
- 2021

The Dirichlet problem for Einstein metrics on cohomogeneity one manifolds

- Mathematics
- 2017

Let $$G{/}H$$G/H be a compact homogeneous space, and let $$\hat{g}_0$$g^0 and $$\hat{g}_1$$g^1 be G-invariant Riemannian metrics on $$G/H$$G/H. We consider the problem of finding a G-invariant…

Ricci flow of warped Berger metrics on $${\mathbb {R}}^{4}$$

- Mathematics
- 2019

We study asymptotically flat SU(2)-cohomogeneity 1 solutions of Ricci flow on $\mathbb{R}^{4}$ whose restrictions to any Euclidean hypersphere are left-invariant Berger spheres. We show that these…

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