Dupin Hypersurfaces in $mathbb R^5$

[摘要] We study Dupinhypersurfaces in $mathbb R^5$ parametrized by lines of curvature, withfour distinct principal curvatures. We characterize locally a genericfamily of such hypersurfaces in terms of the principal curvatures andfour vector valued functions of one variable. We show that these vectorvalued functions are invariant by inversions and homotheties.

[学科分类] 数学（综合）