A Class of Special Hypersurfaces in Real Space Forms

Abstract EN

We define the generalized golden- and product-shaped hypersurfaces in real space forms.

A hypersurface M in real space forms R n + 1 , S n + 1 , and H n + 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.