Conformal deformations of submanifolds in codimension two

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Abstract

Let Mn⊂ Rn+2, \ n≥q 7, be a conformally deformable submanifold of euclidean space in codimension two. In this paper we show that if the submanifold has sufficiently low conformal nullity, a generic conformal condition, then it can be realized as a hypersurface of a conformally 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.

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