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Non-Discrete Complex Hyperbolic Triangle Groups of Type $(n,n, \infty;k)$

Published:2011-05-17
Printed: Jun 2012
• Shigeyasu Kamiya,
Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
• John R. Parker,
University of Durham, South Road, Durham DH1 3LE UK
• James M. Thompson,
University of Durham, South Road, Durham DH1 3LE UK
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Abstract

A complex hyperbolic triangle group is a group generated by three involutions fixing complex lines in complex hyperbolic space. Our purpose in this paper is to improve a previous result and to discuss discreteness of complex hyperbolic triangle groups of type $(n,n,\infty;k)$.
 Keywords: complex hyperbolic triangle group complex hyperbolic triangle group
 MSC Classifications: 51M10 - Hyperbolic and elliptic geometries (general) and generalizations 32M15 - Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 53C55 - Hermitian and Kahlerian manifolds [See also 32Cxx] 53C35 - Symmetric spaces [See also 32M15, 57T15]