A Special class of Hypersurfaces parametrized by lines of curvature in R4 (Selecciones Matemáticas, 2018)
In this paper we study hypersurfaces in R4 parametrized by lines of curvature with three distinct principal curvatures and with Laplace invariants mji = mki = 0; mjik 6= 0 for i; j; k distinct fixed indices. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and three vector valued functions of one variable, this family includes a classe of Dupin hypersurfaces. Moreover, weshow that these vector valued functions are invariant under inversions and homotheties.
Keywords: Dupin hypersurfaces; Laplace invariants; lines of curvature