High rank torus actions on contact manifolds

Abstract

We 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.