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The geometry of complex hyperbolic packs

Published online by Cambridge University Press:  01 July 2009

IOANNIS D. PLATIS
IOANNIS D. PLATIS*
Affiliation:
University of Crete, Heraklion, Crete, Greece. e-mail: [email protected]
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Abstract

Complex hyperbolic packs are hypersurfaces of complex hyperbolic plane H2ℂ which may be considered as dual to the well known bisectors. In this paper we study the geometric aspects associated to packs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 1 , July 2009 , pp. 205 - 234
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

REFERENCES

[1]Aebischer, B. and Miner, R.Deformations of Schottky groups in complex hyperbolic space. Conform. Geom. Dyn. 3 (1999), 24–36.CrossRefGoogle Scholar
[2]Beardon, A. F.The Geometry of Discrete Groups (Springer–Verlag, 1983).CrossRefGoogle Scholar
[3]Do Carmo, M. P.Riemannian Geometry (Birkhäuser, XVI ed 1992).CrossRefGoogle Scholar
[4]Dragomir, S. and Tomassini, G.Differential geometry and analysis on CR manifolds. Progr. Math. 246 (2006).Google Scholar
[5]Falbel, E. and Zocca, V.A Poincaré's polyhedron theorem for complex hyperbolic geometry. J. Reine Angew. Math. 516 (1999) 133–158.CrossRefGoogle Scholar
[6]Goldman, W.Complex Hyperbolic Geometry (Clarendon Press, 1999).CrossRefGoogle Scholar
[7]Gorodski, C. and Gusevskii, N.Complete minimal hypersurfaces in complex hyperbolic space. Manuscripta Math. 103, No. 2 (2000), 221–240.CrossRefGoogle Scholar
[8]Guichard, O.Groups plongés quasi isométriquement dans un group de Lie. Math. Ann. 330(2004) 331–351.CrossRefGoogle Scholar
[9]Kobayashi, S. and Nomizu, K.Foundations of Differential Geometry Vol. I. Interscience Tracts in Pure and Applied Math. 15 (Wiley & Sons, Inc., 1963).Google Scholar
[10]Korányi, A. and Reimann, H. M.Contact transformations as limits of symplectomorphisms. C. R. Acad. Sci. Paris 318 (1994), 1119–1124.Google Scholar
[11]Korányi, A. and Reimann, H. M.Equivariant extension of quasiconformal deformations into the complex unit ball. Indiana Univ. Math. J. 47 (1998), no. 1, 153–176.CrossRefGoogle Scholar
[12]Korányi, A. and Reimann, H. M.Foundations for the theory of quasiconformal mappings of the Heisenberg group. Adv. Math. 111 (1995), 1–87.CrossRefGoogle Scholar
[13]Korányi, A. and Reimann, H. M.Quasiconformal mappings on the Heisenberg group. Invent. Math. 80 (1985), no. 2, 309–338.CrossRefGoogle Scholar
[14]Mostow, G. D.On a remarkable class of fundamental polyhedra in complex hyperbolic plane. Pacific J. Math. 86 (1980), 171–276.CrossRefGoogle Scholar
[15]Parker, J. R. and Platis, I. D.Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space. J. Diff. Geom. 73 (2006), no. 2, 319–350.Google Scholar
[16]Ratcliffe, J. G.Foundations of hyperbolic manifolds. Graduate Texts in Math. 149 (Springer Verlag, 1994).CrossRefGoogle Scholar
[17]Will, P.Thesis: Groupes libres, groupes triangulaires et tore épointé dans PU(2,1). (Université Paris VI, 2006).Google Scholar