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 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.

Manuscript

Contact Fano manifolds and the LeBrun–Salamon conjecture

September 23, 2026 · source · cite as \cite{OAI:Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026}

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.

Result 062 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Agora members.