Hyperbolic n-Manifolds

  • John G. Ratcliffe
Part of the Graduate Texts in Mathematics book series (GTM, volume 149)


In this chapter, we take up the study of hyperbolic n-manifolds. We begin with a geometric method for constructing spherical, Euclidean, and hyperbolic re-manifolds. In Section 11.2, we prove Poincaré’s fundamental polyhedron theorem for freely acting groups. In Section 11.3, we determine the simplices of maximum volume in hyperbolic n-space. In Section 11.4, we study the Gromov invariant of a closed, orientable, hyperbolic manifold. In Section 11.5, we study the measure homology of hyperbolic space-forms. In Section 11.6, we prove Mostow’s rigidity theorem for closed, orientable, hyperbolic manifolds.


Hyperbolic Manifold Convex Polyhedron Fundamental Class Geodesic Line Cusp Point 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John G. Ratcliffe
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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