Geodesic
A characterization of Dupin hypersurfaces in R^5
Serdica Mathematical Journal, Tome 43 (2017) no. 2, pp. 169-186.

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In this paper we study Dupin hypersurfaces in R^5 parametrized by lines of curvature, with four distinct principal curvatures. We give a local characterization of this class of hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. We prove that these vectorial functions describe plane curves or points in R^5. We show that the Lie curvature of these Dupin hypersurfaces is constant with some conditions on the Laplace invariants and the Möbius curvature, but some Möbius curvatures are constant along certain lines of curvature. We give explicit examples of such Dupin hypersurfaces.
Keywords: Dupin hypersurfaces, Lie curvature, Laplace invariants, lines of curvature, 53A07, 53C42 
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     title = {A characterization of {Dupin} hypersurfaces in {R^5}},
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Riveros, Carlos M. C. A characterization of Dupin hypersurfaces in R^5. Serdica Mathematical Journal, Tome 43 (2017) no. 2, pp. 169-186. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_2_a3/