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.
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© 2013 Springer Basel
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Cano, A., Navarrete, J.P., Seade, J. (2013). On the Dynamics of Discrete Subgroups of PU(n, 1). In: Complex Kleinian Groups. Progress in Mathematics, vol 303. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0481-3_7
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DOI: https://doi.org/10.1007/978-3-0348-0481-3_7
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Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-0481-3
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