q-hyperelliptic compact nonorientable Klein surfaces without boundary
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202109173 |
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |