Communications in Analysis and Geometry
Volume 18 (2010)
Genuine deformations of submanifolds II: the conformal case
Pages: 397 – 419
We extend to the conformal realm the concept of genuine deformations ofsubmanifolds, introduced by Dajczer and the first author for theisometric case. Analogously to that case, we call a conformaldeformation of a submanifold $M^n$ genuine if no open subset of $M^n$ canbe included as a submanifold of a higher dimensional conformallydeformable submanifold in such a way that the conformal deformation ofthe former is induced by a conformal deformation of the latter. Wedescribe the geometric structure of a submanifold that admits a genuineconformal deformation and give several applications showing the unifyingcharacter of this concept.