Conformal Immersions for Cmc-Surfaces with the same Gauss Map

An extension of the classic Enneper-Weierstrass representation for conformally parametrised surfaces in 3-dimensional Euclidean space R³ is performed. This is carried out by using CP¹ sigma model, which allows us to study constant mean curvature (CMC) surfaces immersed into R³. In particular it is demonstrated that the generalised Weierstrass representation can admit different CMC-surfaces in R³ which have globally the same Gauss map.