Projective contact classification and the LeBrun–Salamon conjecture
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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 b_2=1 are adjoint varieties with their canonical contact structures, while those with b_2\ge2 have underlying manifold \mathbb P(T^*Z) for a smooth projective variety Z.
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MANUSCRIPT 01
Contact Fano manifolds and the LeBrun–Salamon conjecture
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.…
Full source abstract
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 4m\geq8 is homothetic to a compact symmetric Wolf space.
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