Dupin hypersurfaces with four principal curvatures in \(\mathbb R^{5}\) with principal coordinates (Q1958665)

The authors study Dupin hypersurfaces in a five-dimensional space with four distinct principal curvatures and additional constraints. Assuming that these surfaces are parametrized by lines of curvature the authors derive some results on vector valued functions defined on the surface. Further it turns that out these functions are invariant under inversions and homotheties.