Projective contact classification and the LeBrun–Salamon conjecture

What OpenAI claims

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 b₂=1 are adjoint varieties with their canonical contact structures, while those with b₂ ≥ 2 have underlying manifold ℙ(T^*Z) for a smooth projective variety Z.

Paper

1. Contact Fano manifolds and the LeBrun–Salamon conjecture

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's 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 ≥ 8 is homothetic to a compact symmetric Wolf space.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.