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JØRGENSEN’S INEQUALITY FOR QUATERNIONIC HYPERBOLIC SPACE WITH ELLIPTIC ELEMENTS

Part of: Riemann surfaces

Published online by Cambridge University Press:  02 October 2009

WENSHENG CAO  and
HAIOU TAN
WENSHENG CAO*
Affiliation:
Department of Mathematics and Physics, Wuyi University, Jiangmen 529020, PR China (email: [email protected])
HAIOU TAN
Affiliation:
Department of Mathematics and Physics, Wuyi University, Jiangmen 529020, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we give an analogue of Jørgensen’s inequality for nonelementary groups of isometries of quaternionic hyperbolic space generated by two elements, one of which is elliptic. As an application, we obtain an analogue of Jørgensen’s inequality in the two-dimensional Möbius group of the above case.

Keywords

quaternionic hyperbolic spaceelliptic elementJørgensen’s inequality

MSC classification

Secondary: 30F40: Kleinian groups 57S30: Discontinuous groups of transformations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 121 - 131
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

Supported by NSFs of China (No. 10801107, No. 10671004), NSF of Guangdong Province (No. 8452902001000043) and Educational Commission of Guangdong Province (No. LYM08097). Supported by NSF of Guangdong Province (No. 8152902001000004)

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