2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156160Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifold X inducing a covering family on a submanifold Y with ample normal bundle in X, the main results relate, under suitable conditions, the associated rational connected fiber structures on X and on Y. Applications of these results include an extension theorem for Mori contractions of fiber type and a classification theorem in the case Y has a structure of projective bundle or quadric fibration.27 pages; v2: minor changes and corrections following the referee's comments. v3: few typos corrected. To appear in Math. AnnAlgebraic Geometry14D06, 14J10 (Primary) 14C05, 14J40, 14N30 (Secondary)text