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.
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