All Toric Hermitian ALE Gravitational Instantons
Abstract
Abstract We prove that the only smooth, Ricci flat, ALE gravitational instanton with a toric Hermitian non-Kähler structure is the Eguchi-Hanson instanton. The proof is analogous to the classification of toric Hermitian ALF instantons by Biquard and Gauduchon, although we avoid the use of toric Kähler geometry and instead perform a direct global analysis of the Tod form of the metric in Weyl-Papapetrou coordinates. This supports a conjecture by Gibbons and Bando-Kasue-Nakajima which states that any Ricci flat ALE instanton is self-dual.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Journal of Geometric Analysis
- Volume
- 36
- Issue
- 11
- Publication date
- 3 September 2026
- Language
- EN