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- Title
Discrete subgroups of PU(2, 1) with screw parabolic elements.
- Authors
SHIGEYASU KAMIYA; JOHN R. PARKER
- Abstract
AbstractWe give a version of Shimizu's lemma for groups of complex hyperbolic isometries one of whose generators is a parabolic screw motion. Suppose that Gis a discrete group containing a parabolic screw motion Aand let Bbe any element of Gnot fixing the fixed point of A. Our result gives a bound on the radius of the isometric spheres of Band B?1in terms of the translation lengths of Aat their centres. We use this result to give a sub-horospherical region precisely invariant under the stabiliser of the fixed point of Ain G.
- Subjects
PARABOLIC operators; EXPONENTIAL functions; ISOMETRICS (Mathematics); RADIUS (Geometry); MATHEMATICAL transformations
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2008, Vol 144, Issue 2, p443
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004107000941