Conformal deformations of submanifolds in codimension two
Let M<SUP>n</SUP>⊂ R<SUP>n+2</SUP>, \ 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.
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 52(1), 41-50, 2000-01
The Mathematical Society of Japan