Kähler manifolds with an almost $1/4$-pinched metric
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910679483547648 |
|---|---|
| author | Minemyer, Barry |
| author_facet | Minemyer, Barry |
| contents | In this paper we construct an almost negatively $1/4$-pinched Riemannian metric on a class of compact manifolds recently discovered by Stover and Toledo in [17]. It is known that these manifolds are Kähler and not locally symmetric. These are the first known examples of not locally symmetric Kähler manifolds admitting such a metric and, via the result of Hernandez [9] and Yau and Zheng [18], these manifolds cannot admit a negatively quarter-pinched Riemannian metric. This metric is also interesting because it is a generalization to the complex hyperbolic setting of the famous pinched metric constructed by Gromov and Thurston in [8]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15550 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kähler manifolds with an almost $1/4$-pinched metric Minemyer, Barry Differential Geometry Metric Geometry In this paper we construct an almost negatively $1/4$-pinched Riemannian metric on a class of compact manifolds recently discovered by Stover and Toledo in [17]. It is known that these manifolds are Kähler and not locally symmetric. These are the first known examples of not locally symmetric Kähler manifolds admitting such a metric and, via the result of Hernandez [9] and Yau and Zheng [18], these manifolds cannot admit a negatively quarter-pinched Riemannian metric. This metric is also interesting because it is a generalization to the complex hyperbolic setting of the famous pinched metric constructed by Gromov and Thurston in [8]. |
| title | Kähler manifolds with an almost $1/4$-pinched metric |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2307.15550 |