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Acta Mathematica

, Volume 196, Issue 1, pp 1–64 | Cite as

Cone metrics on the sphere and Livné’s lattices

  • John R. ParkerEmail author
Article

Abstract

We give an explicit construction of a family of lattices in PU (1, 2) originally constructed by Livné. Following Thurston, we construct these lattices as the modular group of certain Euclidean cone metrics on the sphere. We give connections between these groups and other groups of complex hyperbolic isometries.

Keywords

Cone Angle Complex Line Hermitian Form Cone Point Cone Metrics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DurhamEnglandUK

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