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

Journal article

We construct a 2-parameter family of new triaxial SU(2)-invariant complete negative Einstein metrics on the complex line bundle O(-4) over CP1. 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.

Authors: Wang, QS

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Annals of Global Analysis and Geometry
• Volume: 69
• Issue: 3
• Article number: 18
• Publication date: 2026-04-29
• Acceptance date: 2026-03-17
• DOI: 10.1007/s10455-026-10037-4
• EISSN: 1572-9060
• ISSN: 0232704X, 0232-704X
• Language: English