The norm of a Möbius transformation
Published online by Cambridge University Press: 24 October 2008
Extract
A Möbius transformation z → (az + b)/(cz + d), ad — bc = 1, acts as a conformal transformation of the Riemann sphere , and its Poincaré extension acts as an isometry of hyperbolic 3-space modelled in the ball < 1. The size of this transformation can be measured by the matrix norm
or by the hyperbolic distance ρ through which its extension moves the point (0, 0, 0).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 301 - 308
- Copyright
- Copyright © Cambridge Philosophical Society 1984
References
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