Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866911006767185920 |
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| author | González-Álvaro, David Zarei, Masoumeh |
| author_facet | González-Álvaro, David Zarei, Masoumeh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen González-Álvaro, David Zarei, Masoumeh Differential Geometry 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. |
| title | Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2403.13764 |