Computer-assisted construction of SU(2)-invariant negative Einstein metrics
Abstract
Abstract We construct a 2-parameter family of new triaxial SU (2)-invariant complete negative Einstein metrics on the complex line bundle $$\mathcal {O}(-4)$$ O ( - 4 ) over $$\mathbb {C}P^1$$ 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.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Publication details
- Journal / source
- Annals of Global Analysis and Geometry
- Volume
- 69
- Issue
- 3
- Pages
- 18–18
- Publication date
- 1 April 2026
- Language
- EN