Bulletin of the Belgian Mathematical Society - Simon Stevin

A Characterization of Dupin Hypersurfaces in $\mathbb R^4$

Carlos M.C. Riveros

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Abstract

In this paper we study Dupin hypersurfaces in $\mathbb R^4$ parametrized by lines of curvature, with three distinct principal curvatures and $m_{jik}= 0$. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and three vector valued functions of one variable, which are invariant under inversions and homotheties.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 1 (2013), 145-154.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1366306720

Digital Object Identifier
doi:10.36045/bbms/1366306720

Mathematical Reviews number (MathSciNet)
MR3082749

Zentralblatt MATH identifier
1270.35332

Subjects
Primary: 35N10: Overdetermined systems with variable coefficients 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space

Keywords
Dupin hypersurfaces Laplace invariants lines of curvature

Citation

Riveros, Carlos M.C. A Characterization of Dupin Hypersurfaces in $\mathbb R^4$. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 1, 145--154. doi:10.36045/bbms/1366306720. https://projecteuclid.org/euclid.bbms/1366306720


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