2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137580In this paper we prove that, under an explicit integral pinching assumption between the $L^2$-norm of the Ricci curvature and the $L^2$-norm of the scalar curvature, a closed 3-manifold with positive scalar curvature admits an Einstein metric with positive curvature. In particular this implies that the manifold is diffeomorphic to a quotient of ${\Bbb S}^3$.Some misprints in the first version are correctedDifferential GeometryAnalysis of PDEs53C24; 53C20; 53C21; 53C25text