SHIMIZU’S LEMMA FOR COMPLEX HYPERBOLIC SPACE-Reference-Cited by-同舟云学术

SHIMIZU’S LEMMA FOR COMPLEX HYPERBOLIC SPACE

Published:1992-04 Issue:02 Volume:03 Page:291-308
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

PARKER JOHN R.¹

Affiliation:

1. Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA

Abstract

Shimizu’s lemma gives a necessary condition for a discrete group of isometries of the hyperbolic plane containing a parabolic map to be discrete. Viewing the hyperbolic plane as complex hyperbolic 1-space we generalise Shimizu’s lemma to higher dimensional complex hyperbolic space In particular we give a version of Shimizu’s lemma for subgroups of PU (n, 1) containing a vertical translation Partial generalisation to groups containing either an ellipto-parabolic map or non-vertical translations are also given together with examples that show full generalisation is not possible in these cases

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X92000096

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