  The classical classifications of the locally isometrically deformable
Euclidean hypersurfaces obtained by U. Sbrana in 1909 and E. Cartan in 1916
includes four classes, among them the one formed by submanifolds that allow
just a single deformation. The question of whether these Sbrana-Cartan
hypersurfaces do, in fact, exist was not addressed by either of them. Positive
answers to this question were given by Dajczer-Florit-Tojeiro in 1998 for the
ones called of hyperbolic type and by Dajczer-Florit in 2004 when of elliptic
type which is the other possibility. In both cases the examples constructed are
rather special. The main result of this paper yields an abundance of examples
of hypersurfaces of either type and seems to point in the direction of a
classification although that goal remains elusive.
