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Discrete subgroups of PU (2, 1) acting on P 2ℂ and the Kobayashi metric

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Abstract

In this paper, we prove following: If G ⊂ PU (2, 1) is an infinite, discrete group, acting on P 2ℂ without complex invariant lines, then the component containing ℍP 2ℂ of the domain of discontinuity Ω(G) = PP 2ℂ ∖ Λ (G), according to Kulkarni, is G-invariant complete Kobayashi hyperbolic.

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Authors and Affiliations

  1. Facultad de Matemáticas, Anillo Periférico Norte, Universidad Autónoma de Yucatán, Tablaje Cat 13615 Chuburna de Hidalgo, Mérida, Yucatán, México

    Juan Pablo Navarrete & Waldemar Barrera

Authors
  1. Juan Pablo Navarrete
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  2. Waldemar Barrera
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Corresponding author

Correspondence to Juan Pablo Navarrete.

Additional information

The authors were supported by the Universidad Autónoma de Yucatán and the Universidad Nacional Autónoma de México.

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Navarrete, J.P., Barrera, W. Discrete subgroups of PU (2, 1) acting on P 2ℂ and the Kobayashi metric. Bull Braz Math Soc, New Series 40, 99–106 (2009). https://doi.org/10.1007/s00574-009-0005-0

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  • DOI: https://doi.org/10.1007/s00574-009-0005-0

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