Costa, Antonio F.Parlier, Hugo2010-11-302010-11-302010-11-30200810.1112/jlms/jdm100https://infoscience.epfl.ch/handle/20.500.14299/61465WOS:000255084400002We give a geometric characterization of compact Riemann surfaces admitting orientation-reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty real part. We show that there is a family of disjoint simple closed geodesics that intersect all geodesics of a pants decomposition at least twice in uniquely right angles if and only if such an involution exists. This implies that a surface is real if and only if there is a pants decomposition of the surface with all Fenchel-Nielsen twist parameters equal to 0 or 1/2.Riemann SurfacesGeodesicstext::journal::journal article::research article