Communications in Analysis and Geometry

Volume 18 (2010)

Number 2

Genuine deformations of submanifolds II: the conformal case

Pages: 397 – 419



Luis A. Florit (IMPA – Estrada Dona Castorina, Rio de Janeiro, Brazil)

Ruy Tojeiro (Universidade Federal de São Carlos, Brazil)


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.

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