Dupin hypersurfaces with four principal curvatures in R-5 with principal coordinates

作者：Riveros Carlos M C^*

来源：Revista Matematica Complutense, 2010, 23(2): 341-354.

DOI：10.1007/s13163-009-0023-x

• Dupin hypersurfaces
• Laplace invariants
• Lines of curvature

In this paper we study Dupin hypersurfaces in R-5 parametrized by lines of curvature, with four distinct principal curvatures and T-ijkl = 0. We characterize locally a family of such hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. Moreover, we show that these vector valued functions are invariant under inversions and homotheties.

• 出版日期2010-7