On the structure of non-Euclidean crystallographic groups

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 .