On a special class of hypersurfaces in R5 - C. Riveros, Carlos M. (2025)
In this paper we study hypersurfaces in R5 parametrized by lines of curvature, with four distinct principal curvatures and with Laplace invariants mji = mki = mli = 0, mjik ̸= 0, mjkl ̸= 0, mljk ̸= 0, Tijkl ̸= 0 for i, j, k, l distinct fixed indices. We characterize locally a generic 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. We observe that this class of hypersurfaces cannot have constant Mobius curvature.