Orientation reversing square roots of involutions
Robert Zarrow · Illinois Journal of Mathematics · 1979
We say that a Riemann surface is embeddable if it is conformally equivalent to a smooth surface which is embedded in R3.If f is an orientation preserving self-homeomorphism of a smooth surface X, then we say f is metrically embeddable if there exists a smooth injection d" X---l 3 so that dfd -1 is the restriction of a rotation.If f is orientation reversing, then we say that f is metrically embeddable if dfdis the restriction of a reflection in some plane.Finally, if X is a Riemann surface, f is conformal or anti-conformal and d is conformal, then we simply say that f is embeddable.