Slant geometry of spacelike hypersurfaces in hyperbolic space and de Sitter space (Q427929)

The authors consider a one-parameter family of new extrinsic differential geometries on hypersurfaces in hyperbolic space. Recently, the second author and his collaborators have constructed a new geometry which is called horospherical geometry on hyperbolic space. There is another geometry which is the famous Gauss-Bolyai-Lobachevski geometry (i.e., the hyperbolic geometry) on hyperbolic space. The slant geometry is a one-parameter family of geometries which connects these two geometries. Moreover, the authors construct a one-parameter family of geometries on space-like hypersurfaces in de Sitter space.