Geometry and topology · Oct 6, 2026

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.

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openai/math catalogue entry ↗