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On the structure of non-Euclidean crystallographic groups

Published online by Cambridge University Press:  24 October 2008

David Singerman
Affiliation:
The University, Southampton

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
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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