Nagoya Mathematical Journal

Conformally flat hypersurfaces in Euclidean 4-space

Yoshihiko Suyama

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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.

Article information

Nagoya Math. J., Volume 158 (2000), 1-42.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]


Suyama, Yoshihiko. Conformally flat hypersurfaces in Euclidean 4-space. Nagoya Math. J. 158 (2000), 1--42.

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