On the structure of non-Euclidean crystallographic groups
- 1 July 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 76 (1) , 233-240
- https://doi.org/10.1017/s0305004100048891
Abstract
Let denote the group of transformations of the upper-half complex plane U onto itself of the formIf, 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 .Keywords
This publication has 4 references indexed in Scilit:
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- Symmetries of Riemann surfaces with large automorphism groupMathematische Annalen, 1974
- The Classification of Non-Euclidean Plane Crystallographic GroupsCanadian Journal of Mathematics, 1967
- On non-Euclidean crystallographic groupsMathematische Zeitschrift, 1966