High rank torus actions on contact manifolds

Gianluca Occhetta, Eleonora A. Romano, Luis E. Solá Conde, Jarosław A. Wiśniewski
2021 Selecta Mathematica, New Series  
AbstractWe prove LeBrun–Salamon conjecture in the following situation: if X is a contact Fano manifold of dimension $$2n+1$$ 2 n + 1 whose group of automorphisms is reductive of rank $$\ge \max (2,(n-3)/2)$$ ≥ max ( 2 , ( n - 3 ) / 2 ) then X is the adjoint variety of a simple group. The rank assumption is fulfilled not only by the three series of classical linear groups but also by almost all the exceptional ones.
doi:10.1007/s00029-021-00621-w fatcat:rmdo52mx5rdsbeyajzbsgaxwvm