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Conformally flat hypersurfaces in Euclidean 4-space

Published online by Cambridge University Press:  22 January 2016

Yoshihiko Suyama
Yoshihiko Suyama*
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-0180, Japan, suyama@fukuoka-u.ac.jp
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Abstract

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We study generic and conformally flat hypersurfaces in Euclidean four-space. What kind of conformally flat three manifolds are really immersed generically and conformally in Euclidean space as hypersurfaces? According to the theorem due to Cartan [1], there exists an orthogonal curvature-line coordinate system at each point of such hypersurfaces. This fact is the first step of our study. We classify such hypersurfaces in terms of the first fundamental form. In this paper, we consider hypersurfaces with the first fundamental forms of certain specific types. Then, we give a precise representation of the first and the second fundamental forms of such hypersurfaces, and give exact shapes in Euclidean space of them.

Keywords

53A3053B2553C4053C42
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 158 , December 2000 , pp. 1 - 42
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

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