Manifolds with PIC1 pinched curvature
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908360906899456 |
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| author | Lee, Man-Chun Topping, Peter M. |
| author_facet | Lee, Man-Chun Topping, Peter M. |
| contents | Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton. In this paper we generalise our work on the existence of Ricci flows from non-compact pinched three-manifolds in order to prove a higher-dimensional analogue. We construct a solution to Ricci flow, for all time, starting with an arbitrary complete non-compact manifold that is PIC1 pinched. As an application we prove that any complete manifold of non-negative complex sectional curvature that is PIC1 pinched must be flat or compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07623 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Manifolds with PIC1 pinched curvature Lee, Man-Chun Topping, Peter M. Differential Geometry 53E20, 53C20, 53C21 Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton. In this paper we generalise our work on the existence of Ricci flows from non-compact pinched three-manifolds in order to prove a higher-dimensional analogue. We construct a solution to Ricci flow, for all time, starting with an arbitrary complete non-compact manifold that is PIC1 pinched. As an application we prove that any complete manifold of non-negative complex sectional curvature that is PIC1 pinched must be flat or compact. |
| title | Manifolds with PIC1 pinched curvature |
| topic | Differential Geometry 53E20, 53C20, 53C21 |
| url | https://arxiv.org/abs/2211.07623 |