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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.21644 |
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| _version_ | 1866915968760938496 |
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| author | Wang, Qiu Shi |
| author_facet | Wang, Qiu Shi |
| contents | We construct a 2-parameter family of new triaxial $SU(2)$-invariant complete negative Einstein metrics on the complex line bundle $\mathcal{O}(-4)$ over $\mathbb{C}P^1$. The metrics are conformally compact and neither Kähler nor self-dual. The proof involves using rigorous numerics to produce an approximate Einstein metric to high precision in a bounded region containing the singular orbit or "bolt", which is then perturbed to a genuine Einstein metric using fixed-point methods. At the boundary of this region, the latter metric is sufficiently close to hyperbolic space for us to show that it indeed extends to a complete, asymptotically hyperbolic Einstein metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computer-assisted construction of $SU(2)$-invariant negative Einstein metrics Wang, Qiu Shi Differential Geometry 53C25, 65D15 We construct a 2-parameter family of new triaxial $SU(2)$-invariant complete negative Einstein metrics on the complex line bundle $\mathcal{O}(-4)$ over $\mathbb{C}P^1$. The metrics are conformally compact and neither Kähler nor self-dual. The proof involves using rigorous numerics to produce an approximate Einstein metric to high precision in a bounded region containing the singular orbit or "bolt", which is then perturbed to a genuine Einstein metric using fixed-point methods. At the boundary of this region, the latter metric is sufficiently close to hyperbolic space for us to show that it indeed extends to a complete, asymptotically hyperbolic Einstein metric. |
| title | Computer-assisted construction of $SU(2)$-invariant negative Einstein metrics |
| topic | Differential Geometry 53C25, 65D15 |
| url | https://arxiv.org/abs/2504.21644 |