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Global Geometrical Coordinates on Falbel's Cross-Ratio Variety

Published online by Cambridge University Press:  20 November 2018

John R. Parker  and
Ioannis D. Platis
John R. Parker
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom e-mail: j.r.parker@dur.ac.uk
Ioannis D. Platis
Affiliation:
Department of Mathematics, Aristotle University of Salonica, Salonica, Greece e-mail: johnny_platis@yahoo.com.au
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Abstract

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Falbel has shown that four pairwise distinct points on the boundary of a complex hyperbolic 2-space are completely determined, up to conjugation in $\text{PU}\left( 2,\,1 \right)$, by three complex cross-ratios satisfying two real equations. We give global geometrical coordinates on the resulting variety.

Keywords

32G0532M05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 2 , 01 June 2009 , pp. 285 - 294
Copyright
Copyright © Canadian Mathematical Society 2009

References

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