2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77567We prove that a projective contact manifold X with second Betti number at least 2 whose canonical bundle K_X is not nef, is always the projectivised tangent bundle P(T_Y) of a projective manifold Y. It is expected that the canonical bundle of a projective contact manifold is never nef; we prove this unless possibly K_X^2 = 0 and K_X is not numerically trivial. Moreover we study more generally nef subsheaves of rank 1 in the cotangent bundle which are proportional to the canonical bundle.LaTeX 2e, revised versionAlgebraic Geometry14M99 (Primary) 53C55 53C25 32J18 (Secondary)text