International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 4, Pages 215-227
doi:10.1155/S0161171202109173
q-hyperelliptic compact nonorientable Klein
surfaces without boundary
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.
Abstract
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.