Hypersurfaces of the spherical type degenerated
DOI:
https://doi.org/10.17268/sel.mat.2020.02.03Keywords:
EDSGW-surfaces, surfaces of the spherical type, support function, planar lines of curvatureAbstract
In this work, we dene 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 characterizethe DST-hypersurfaces through a diferential 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.
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