A Class of Special Hypersurfaces in Real Space Forms

Abstract

We define the generalized golden- and product-shaped hypersurfaces in real space forms. A hypersurface M in real space forms Rn+1, Sn+1, and Hn+1 is isoparametric if it has constant principal curvatures. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the generalized golden- and product-shaped hypersurfaces in real space forms.