A classification of hyperbolic manifolds related to the three-dimensional torus

Akira Ushijima

Published 2004-06-04Version 1

L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete classification up to isometry, and also their isometry groups. The key tool is the so-called canonical decomposition of hyperbolic manifolds.