Work

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

Year: 2026

Type: article

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.

Source: Annals of Global Analysis and Geometry

DOI: 10.1007/s10455-026-10037-4

Author: Qiu Shi Wang

Institution: University of Oxford

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Engineering and Physical Sciences Research Council, Fonds de recherche du Québec – Nature et technologies