Hypersurfaces of the spherical type degenerated

Abstract

In this work, we define the hypersurfaces of the spherical type degenerated (in short DST-hypersurfaces), these hypersurfaces has the geometric property that the middle spheres pass through the origin of the Euclidean space. We present a representation for these hypersurfaces in the case where the stereographic projection of the Gauss map N is given by the identity application. We characterize the DST-hypersurfaces through a differential equation and we give an explicit example of a two-parameter family of DST-hypersurfaces with planar lines of curvature foliated by (n-1)-dimensional spheres. Moreover, we classify the DST hypersurfaces of rotation.

Keywords

• edsgw-surfaces
• surfaces of the spherical type
• support function
• planar lines of curvature