Family 062Algebraic and complex geometryNo LeanNot yet digested
Projective contact classification and the LeBrun–Salamon conjecture
Proves the LeBrun–Salamon conjecture: every closed connected positive quaternionic-Kähler manifold of real dimension at least eight is homothetic to a compact symmetric Wolf space. It also proves contact-Fano homogeneity and classifies smooth connected complex projective contact manifolds of complex dimension at least three: those with are adjoint varieties with their canonical contact structures, while those with have underlying manifold for a smooth projective variety Z.
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Contact Fano manifolds and the LeBrun–Salamon conjecture
Sep 23, 2026·paper.pdf
We resolve the contact-Fano homogeneity conjecture and the Riemannian LeBrun–Salamon conjecture positively. Every smooth connected complex projective contact Fano manifold of complex dimension at least three, with its given contact distribution, is contact-isomorphic to the adjoint variety of a simple complex Lie algebra. Consequently, every closed connected smooth positive quaternionic-Kähler manifold of real dimension is homothetic to a compact symmetric Wolf space.