On H-balls and canonical regions of loxodromic elements in complex hyperbolic space
Published online by Cambridge University Press: 24 October 2008
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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