Embeddable anticonformal automorphisms of Riemann surfaces

Abstract

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 $e:S\to {\mathbf{E}}^3$ 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].