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 automorphisms reductive rank $$\ge \max (2,(n-3)/2)$$ ≥ max ( , - 3 ) / then adjoint variety simple group. The assumption fulfilled not only by three series classical linear groups but also almost all exceptional ones.