Conformal deformations of submanifolds in codimension two

Let M-n subset of Rn+2, n greater than or equal to 7, be a conformally defo rmable submanifold of euclidean space in codimension two. In this paper we show that if the submanifold has sufficiently low conformal nullity, a gene ric conformal condition, then it can be realized as a hypersurface of a con formally deformable hypersurface. The latter have been classified by Cartan early this century. Furthermore, it turns out that all deformations of the former are induced by deformations of the latter.