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On the Dynamics of Discrete Subgroups of PU(n, 1)

  • Angel Cano
  • Juan Pablo Navarrete
  • José Seade
Chapter
Part of the Progress in Mathematics book series (PM, volume 303)

Abstract

If G is a discrete subgroup of PU(n, 1) ⊂ PSL(n+1,\(\mathbb{C}\)), then it acts on the complex projective space \(\mathbb{P}^{n}_\mathbb{C}\) preserving the unit ball \(\{[{z_0}:{z_2}:\ldots :{z_n}]\in {P^n_\mathbb{C}}|{|{z_1}|^2}+\ldots+{|{z_1}|^2}<{|{z_0}|^2}\}\) which can be equipped with the Bergman metric and provides a model for the complex hyperbolic space \(\mathbb{H}^{n}_\mathbb{C}\), with PU(n, 1) as its group of holomorphic isometries.

Keywords

Distinct Element Discrete Group Cluster Point Discrete Subgroup Geodesic Segment 
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 Basel 2013

Authors and Affiliations

  • Angel Cano
    • 1
  • Juan Pablo Navarrete
    • 2
  • José Seade
    • 1
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de México Unidad CuernavacaCuernavacaMexico
  2. 2.Facultad de MatemáticasUniversidad Autónoma de YucatánMéridaMexico

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