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Dupin Hypersurfaces in ${{\mathbb{R}}^{5}}$

Published online by Cambridge University Press:  20 November 2018

Carlos M.C. Riveros  and
Keti Tenenblat
Carlos M.C. Riveros
Affiliation:
Departamento de Matemática, Universidade Federal do Tocantins, 77330-000, Arraias, TO, Brazil, e-mail: [email protected]
Keti Tenenblat
Affiliation:
Departamento de Matemática, Universidade de Brasília, 70910-900, Brasília, DF, Brazil, e-mail: [email protected]
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Abstract

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We study Dupin hypersurfaces in ${{\mathbb{R}}^{5}}$ parametrized by lines of curvature, with four distinct principal curvatures. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. We show that these vector valued functions are invariant by inversions and homotheties.

Keywords

53B2553C4235N1037K10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 6 , 01 December 2005 , pp. 1291 - 1313
Copyright
Copyright © Canadian Mathematical Society 2005

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