Isometric immersions of H-1(n) into H-1(n+1)

The complete codimension 1 totally geodesic laminations of the hyperquadrics of constant curvature 1 or -1 are completely determined. Also the set of all codimension 1 isometric immersions of a hyperquadric into another of the same constant curvature are determined and characterized in terms of the naturally associated totally geodesic laminations and the curvature of the laminations. Note that the hyperquadrics of constant curvature 1 and -1 are often called the de Sitter space-time and the anti de Sitter space-time, respectively.