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arXiv · 2403.13764

Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen

David González-Álvaro·Masoumeh Zarei
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Abstract

We prove that there exist $\mathsf{SU}_{3}$-invariant metrics on Aloff-Wallach spaces $W^7_{k_1, k_2}$, as well as $\mathsf{SU}_{5}$-invariant metrics on the Berger space $B^{13}$, which have positive sectional curvature and evolve under the Ricci flow to metrics with non-positively curved planes.

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David González-Álvaro, Masoumeh Zarei. 2024-03-20. Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen. https://arxiv.org/abs/2403.13764

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