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On H-balls and canonical regions of loxodromic elements in complex hyperbolic space

Published online by Cambridge University Press:  24 October 2008

Shigeyasu Kamiya
Shigeyasu Kamiya
Affiliation:
Department of Mechanical Engineering, Okayama University of Science, 1-1 Ridai-cho Okayama 700, Japan Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, CambridgeCB2 1SB
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Extract

Let U(1, n; ℂ) be the automorphism group of the Hermitian form

for . We can regard an element of U(1, n; ℂ) as a transformation acting on , where is the closure of the complex unit ball

The non-trivial elements of U(1, n; ℂ) fall into three conjugacy types, depending on the number and the location of their fixed points. Let g be a non-trivial element of U(1, n; ℂ). We call g elliptic if it has a fixed point in Bn and g parabolic if it has exactly one fixed point and this lies on the boundary ∂Bn. An element g will be called loxodromic if it has exactly two fixed points and they lie on ∂Bn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 573 - 582
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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