Positive intermediate curvatures and Ricci flow
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912322693365760 |
|---|---|
| author | González-Álvaro, David Zarei, Masoumeh |
| author_facet | González-Álvaro, David Zarei, Masoumeh |
| contents | 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 Böhm and Wilking in the case of $n=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08641 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positive intermediate curvatures and Ricci flow González-Álvaro, David Zarei, Masoumeh Differential Geometry 53C21 (Primary), 53E20 (Secondary) 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 Böhm and Wilking in the case of $n=2$. |
| title | Positive intermediate curvatures and Ricci flow |
| topic | Differential Geometry 53C21 (Primary), 53E20 (Secondary) |
| url | https://arxiv.org/abs/2303.08641 |