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On the structure of non-Euclidean crystallographic groups

Published online by Cambridge University Press:  24 October 2008

David Singerman
David Singerman
Affiliation:
The University, Southampton
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Extract

Let denote the group of transformations of the upper-half complex plane U onto itself of the form

If, on U, we introduce the Riemannian metric ds = |dz| y−1 (z = x + iy), then U becomes a model of the hyperbolic plane and its group of isometries. The set of elements of type I, the orientation-preserving isometries form a subgroup of index two in , which we denote by .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 233 - 240
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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(5)Wilkie, H. C.On non-Euclidean crystallographic groups. Math. Z. 91 (1966), 87–102.CrossRefGoogle Scholar