## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Carlos M.C. Riveros

#### 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

https://projecteuclid.org/euclid.bbms/1366306720

Digital Object Identifier
doi:10.36045/bbms/1366306720

Mathematical Reviews number (MathSciNet)
MR3082749

Zentralblatt MATH identifier
1270.35332

#### 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