Commentarii Mathematici Helvetici

, Volume 72, Issue 2, pp 203–215 | Cite as

Embeddable anticonformal automorphisms of Riemann surfaces

  • A. F. Costa


Let S be a Riemann surface and f be an automorphism of finite order of S. We call f embeddable if there is a conformal embedding \( e : S \to \bf {E}^3 \) such that \( e \circ f \circ e^{-1} \) is the restriction to e(S) of a rigid motion. In this paper we show that an anticonformal automorphism of finite order is embeddable if and only if it belongs to one of the topological conjugation classes here described. For conformal automorphisms a similar result was known by R.A. Rüedy [R3].

Keywords. Riemann surface, anticonformal automorphism, conformal embedding. 


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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • A. F. Costa
    • 1
  1. 1.Departamento de Matemáticas Fundametales, Facultad de Ciencias, UNED, C/Senda del Rey, s/n, E-28040 Madrid, SpainSpain

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