2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225308We show that among the Euclidean submanifolds with codimension two the ones of rank two that are parabolic but nonruled are isometrically rigid. This generalizes the result in [10] that these submanifolds are genuinely rigid. In addition, we give a parametric classifications of all parabolic submanifolds.14 pages. To appear in Mich. Math. JDifferential Geometrytext