Slant Geometry of Spacelike Hypersurfaces in Hyperbolic space and de Sitter space

We consider a one-parameter family of new extrinsic differential geometries\ud on hypersurfaces in Hyperbolic space. Recently, the second author and his collaborators have\ud constructed a new geometry which is called horospherical geometry on Hyperbolic space.\ud There is another geometry which is the famous Gauss-Boryay-Robechevski geometry (i.e., the\ud hyperbolic geometry) on Hyperbolic space. The slant geometry is a one-parameter family of geometries which\ud connect these two geometries. Moreover, we construct a one-parameter family of geometries on\ud spacelike hypersurfaces in de Sitter space