Abstract
In this chapter, we study the geometry of geometrically finite hyperbolic n-manifolds. The chapter begins with a study of the limit set of a discrete group of Möbius transformations of B n. In Section 12.3, we study geometrically finite groups of Möbius transformations of B n. In Section 12.4, we study nilpotent groups of isometries of hyperbolic n-space. In Section 12.5, we prove the Margulis lemma. In Section 12.6, we apply the Margulis lemma to study the geometry of geometrically finite hyperbolic n-manifolds. In particular, we determine the global geometry of complete hyperbolic n-manifolds of finite volume.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ratcliffe, J.G. (1994). Geometrically Finite n-Manifolds. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4013-4_12
Download citation
DOI: https://doi.org/10.1007/978-1-4757-4013-4_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94348-0
Online ISBN: 978-1-4757-4013-4
eBook Packages: Springer Book Archive