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arXiv · 2303.08641

Positive intermediate curvatures and Ricci flow

David González-Álvaro·Masoumeh Zarei
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Abstract

We show that, for any $n\geq 2$, there exists a homogeneous space of dimension $d=8n-4$ with metrics of $\mathrm{Ric}_{\frac{d}{2}-5}>0$ if $n\neq 3$ and $\mathrm{Ric}_6>0$ if $n=3$ which evolve under the Ricci flow to metrics whose Ricci tensor is not $(d-4)$-positive. Consequently, Ricci flow does not preserve a range of curvature conditions that interpolate between positive sectional and positive scalar curvature. This extends a theorem of B\"ohm and Wilking in the case of $n=2$.

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David González-Álvaro, Masoumeh Zarei. 2023-03-15. Positive intermediate curvatures and Ricci flow. https://arxiv.org/abs/2303.08641

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