Some Hyperbolic 3-Manifolds with Totally Geodesic Boundary

Abstract

We construct a family of compact hyperbolic 3-manifolds with totally geodesic boundary, depending on three integer parameters. Then we determine geometric presentations of the fundamental groups of these manifolds and prove that they are cyclic coverings of the 3-ball branched along a specified tangle with two components. Finally, we give a classification of these manifolds up to homeomorphism (resp., isometry), and determine their isometry groups.