  We extend to the conformal realm the concept of genuine deformations of
submanifolds, introduced by Dajczer and the first author for the isometric
case. Analogously to that case, we call a conformal deformation of a
submanifold $M^n$ genuine if no open subset of $M^n$ can be included as a
submanifold of a higher dimensional conformally deformable submanifold in such
a way that the conformal deformation of the former is induced by a conformal
deformation of the latter. We describe the geometric structure of a submanifold
that admits a genuine conformal deformation and give several applications
showing the unifying character of this concept.

Differential Geometry