We prove that alternating links with two totally geodesic checkerboard surfaces are three projection the 1-skeleton of octahedron, cuboctahedron and icosidodecahedron. also characterize these as right-angled completely realisable show all hyperbolic weaving knots exceptions have both not geodesic.

In this paper we modify the maximum principal of (Galloway, 2000) for totally geodesic null hypersurfaces by proving a geometric maximum principle which obeys mean curvature inequalities of a family of totally umbilical null hypersurfaces of a spacetime manifold (Theorem 6). As a physical interpretation we show that, in particular, for a prescribed class of spacetimes the geometric inequality o...