Prime order automorphisms of Klein surfaces representable by rotations of the euclidean space

Abstract

Let S be a bordered orientable Klein surface and p a prime. Assume that f is an order p automorphism of S. In this work we obtain the conditions on the topological type of (S,f) to be conformally equivalent to (S',f') where S' is a bordered orientable Klein surface embedded in the Euclidean space and f' is the restriction to S' of a prime order rotation. We represent two famous automorphisms using rotations of R^4 and S^4 : the order seven automorphisms of the Klein quartic and the Wiman surface.