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arXiv · 2504.18475

Quasi-Einstein structures and Hitchin's equations

Alex Colling·Maciej Dunajski
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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 \cite{DL23} 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 $S^2 \times S^1$.

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Alex Colling, Maciej Dunajski. 2025-04-25. Quasi-Einstein structures and Hitchin's equations. https://arxiv.org/abs/2504.18475

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