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

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

Received 21 September 2001

Copyright © 2002 Hindawi Publishing Corporation. 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 acompact nonorientable surface with a dianalytic structure definedon 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 ordertwo such that the quotient X-〈Φ〉 has algebraic genus q. q-hyperelliptic nonorientable KSs without boundarynonorientable Riemann surfaces were characterized by means ofnon-Euclidean crystallographic groups. In this paper, using thatcharacterization, we determine bounds for the order of theautomorphism group of a nonorientable q-hyperelliptic Klein surface X such that X-〈Φ〉 has no boundary andprove that the bounds are attained. Besides, we obtain thedimension of the Teichmüller space associated to this type of surfaces.





Autor: J. A. Bujalance and B. Estrada

Fuente: https://www.hindawi.com/



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