Geodesic
Dupin Hypersurfaces in ${{\mathbb{R}}^{5}}$
Canadian journal of mathematics, Tome 57 (2005) no. 6, pp. 1291-1313

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2005-052-1
Mots-clés : 53B25, 53C42, 35N10, 37K10 
Riveros, Carlos M.C.; Tenenblat, Keti. Dupin Hypersurfaces in ${{\mathbb{R}}^{5}}$. Canadian journal of mathematics, Tome 57 (2005) no. 6, pp. 1291-1313. doi: 10.4153/CJM-2005-052-1
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