Generalized m-quasi-Einstein manifolds have Killing potential vector fields under integral assumptions, with divergence-free fields also Killing, sign-based triviality results, a corrected Ghosh theorem, and rigidity for geodesic potentials.
Quasi-Einstein structures and Hitchin's equations
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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 $S^2 \times S^1$.
fields
math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Generalized m-quasi-Einstein manifolds of Yamabe-type have potential vector fields that vanish or are non-trivial Killing fields under natural assumptions in compact and non-compact settings.
citing papers explorer
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On Generalized Quasi-Einstein Manifolds
Generalized m-quasi-Einstein manifolds have Killing potential vector fields under integral assumptions, with divergence-free fields also Killing, sign-based triviality results, a corrected Ghosh theorem, and rigidity for geodesic potentials.
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On the rigidity of generalized $m$-quasi-Einstein manifolds of Yamabe-type
Generalized m-quasi-Einstein manifolds of Yamabe-type have potential vector fields that vanish or are non-trivial Killing fields under natural assumptions in compact and non-compact settings.