“…Following Long and Reid [21,22], we say that a hyperbolic n-manifold M bounds geometrically if it is isometric to ∂W , for a hyperbolic (n + 1)-manifold W with totally geodesic boundary. This class of hyperbolic manifolds has attracted significant interest, and for n = 3 some progress has been recently done -see [18,19,23,26,34,35].…”