q -hyperelliptic compact nonorientable Klein surfaces without boundary

J. A. Bujalance and B. Estrada

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-13

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:830615

DOI: 10.1155/S0161171202109173

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