Quasi-Einstein Structures and Hitchin’s Equations
Abstract
Abstract We prove (Theorem 1.1.) that a class of quasi-Einstein structures on closed manifolds must admit a Killing vector field. This extends the rigidity theorem obtained in [20] for the extremal black hole horizons and completes the classification of compact quasi-Einstein 2-manifolds in this class. We also explore special cases of the quasi-Einstein equations related to integrability and the Hitchin equations, as well as to Einstein-Weyl structures and Kazdan-Warner type PDEs. This leads to novel explicit examples of quasi-Einstein structures on (non-compact) 2-manifolds and on $$S^2 \times S^1$$ S 2 × S 1 .
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 9
- Publication date
- 1 August 2026
- Language
- EN