Automorphisms of Klein Surfaces of Algebraic Genus One

Authors : Adnan MELEKOĞLU

Pages : 71-78

View : 15 | Download : 12

Publication Date : 2006-04-01

Article Type : Research Paper

Abstract :Cebirsel cinsi bir olan Klein yüzeyleri; Möbius şeridi, silindir ve Klein şişesidir. Bu çalışmada bu yüzeylerin otomorfizmaları belirlenmiştir.Let X be a compact Riemann surface of genusg ≥ 1 . An automorphism of X is a conformal or anti-conformal homeomorphism f : X → X . X is called symmetric if it admits an anti-conformal involution s : X → X which we call a symmetry of X . The quotient surface S = X /〈s〉 is a Klein surface. By a Klein surface we mean a surface with a dianalytic structure insert ignore into journalissuearticles values(see [1]);. Here X is called the complex double of S . The algebraic genus of S is then defined to be the topological genus of X . It is known that the Klein surfaces of algebraic genus one are the Möbius band, the annulus and the Klein bottle. In this paper we study the automorphisms of these surfaces. We do not claim originality of the work. However, it contains something demonstrative of the method, not readily available in the literature, which may be helpful to those who are not experts but wish to understand the subject.
Keywords : Klein yüzeyi, Möbius şeridi, silindir, Klein şişesi, otomorfizma