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Dupin Hypersurfaces in $\mathbb R^5$ |
Canad. J. Math. 57(2005), 1291-1313
Published:2005-12-01
Printed: Dec 2005
Printed: Dec 2005
- Carlos M. C. Riveros
- Keti Tenenblat
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.) |