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# Dupin Hypersurfaces in $\mathbb R^5$

Published:2005-12-01
Printed: Dec 2005
• Carlos M. C. Riveros
• Keti Tenenblat
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## Abstract

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.
 MSC Classifications: 53B25 - Local submanifolds [See also 53C40] 53C42 - Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 35N10 - Overdetermined systems with variable coefficients 37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

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