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

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