%0 Journal Article %T Isometric rigidity in codimension two %A Marcos Dajczer %A Pedro Morais %J Mathematics %D 2009 %I arXiv %X We 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. %U http://arxiv.org/abs/0903.5528v1