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arXiv · 2504.21644

Computer-assisted construction of $SU(2)$-invariant negative Einstein metrics

Qiu Shi Wang
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Abstract

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 K\"ahler 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.

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Qiu Shi Wang. 2025-04-30. Computer-assisted construction of $SU(2)$-invariant negative Einstein metrics. https://doi.org/10.1007/s10455-026-10037-4

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