International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 4, Pages 215-227

q-hyperelliptic compact nonorientable Klein surfaces without boundary

J. A. Bujalance and B. Estrada

Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, Paseo Senda del Rey 9, Madrid 28040, Spain

Received 21 September 2001

Copyright © 2002 J. A. Bujalance and B. Estrada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X be a nonorientable Klein surface (KS in short), that is a compact nonorientable surface with a dianalytic structure defined on it. A Klein surface X is said to be q-hyperelliptic if and only if there exists an involution Φ on X (a dianalytic homeomorphism of order two) such that the quotient X/Φ has algebraic genus q. q-hyperelliptic nonorientable KSs without boundary (nonorientable Riemann surfaces) were characterized by means of non-Euclidean crystallographic groups. In this paper, using that characterization, we determine bounds for the order of the automorphism group of a nonorientable q-hyperelliptic Klein surface X such that X/Φ has no boundary and prove that the bounds are attained. Besides, we obtain the dimension of the Teichmüller space associated to this type of surfaces.