Journal of the Mathematical Society of Japan

Conformal deformations of submanifolds in codimension two

Marcos DAJCZER and Ruy TOJEIRO

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Abstract

Let MnRn+2,n7, 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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107654

Digital Object Identifier
doi:10.2969/jmsj/05210041

Mathematical Reviews number (MathSciNet)
MR1727201

Zentralblatt MATH identifier
0955.53010

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53A30: Conformal differential geometry

Keywords
Conformal immersion conformal deformation Cartan hypersurface

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


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