An explicit description of the Kähler-Einstein metrics of Guenancia-Hamenstädt
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913814757244928 |
|---|---|
| author | Lafont, Jean-François Minemyer, Barry |
| author_facet | Lafont, Jean-François Minemyer, Barry |
| contents | Fine and Premoselli (FP) constructed the first examples of manifolds that do not admit a locally symmetric metric but do admit a negatively curved Einstein metric. The manifolds here are hyperbolic branched covers like those used by Gromov and Thurston, and the construction of their model Einstein metric is a variation of the hyperbolic metric written in polar coordinates. Very recently, Guenancia and Hamenstädt (GH) proved the existence of the first examples of manifolds that are not locally symmetric but admit a negatively curved Kähler-Einstein metric. The GH metrics are realized on complex hyperbolic branched covers constructed by Stover and Toledo. In this article we generalize the construction of FP to the complex hyperbolic setting and show that this yields a negatively curved Einstein metric that asymptotically approaches the metric of GH. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An explicit description of the Kähler-Einstein metrics of Guenancia-Hamenstädt Lafont, Jean-François Minemyer, Barry Differential Geometry Mathematical Physics Geometric Topology Metric Geometry Primary 53C25, 53C35, 51M15, Secondary 53C55, 53B20, 57R18 Fine and Premoselli (FP) constructed the first examples of manifolds that do not admit a locally symmetric metric but do admit a negatively curved Einstein metric. The manifolds here are hyperbolic branched covers like those used by Gromov and Thurston, and the construction of their model Einstein metric is a variation of the hyperbolic metric written in polar coordinates. Very recently, Guenancia and Hamenstädt (GH) proved the existence of the first examples of manifolds that are not locally symmetric but admit a negatively curved Kähler-Einstein metric. The GH metrics are realized on complex hyperbolic branched covers constructed by Stover and Toledo. In this article we generalize the construction of FP to the complex hyperbolic setting and show that this yields a negatively curved Einstein metric that asymptotically approaches the metric of GH. |
| title | An explicit description of the Kähler-Einstein metrics of Guenancia-Hamenstädt |
| topic | Differential Geometry Mathematical Physics Geometric Topology Metric Geometry Primary 53C25, 53C35, 51M15, Secondary 53C55, 53B20, 57R18 |
| url | https://arxiv.org/abs/2505.00517 |