## Journal of the Mathematical Society of Japan

### Conformal deformations of submanifolds in codimension two

#### Abstract

Let $M^{n}\subset R^{n+2},$$n\geq 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 52, Number 1 (2000), 41-50.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213107654

Digital Object Identifier
doi:10.2969/jmsj/05210041

Mathematical Reviews number (MathSciNet)
MR1727201

Zentralblatt MATH identifier
0955.53010

#### Citation

DAJCZER, Marcos; TOJEIRO, Ruy. Conformal deformations of submanifolds in codimension two. J. Math. Soc. Japan 52 (2000), no. 1, 41--50. doi:10.2969/jmsj/05210041. https://projecteuclid.org/euclid.jmsj/1213107654