On analytic descriptions of two-dimensional surfaces associated with the sigma model

We study analytic descriptions of conformal immersions of the Riemann sphere S2 into the sigma model. In particular, an explicit expression for two-dimensional (2D) surfaces, obtained from the generalized Weierstrass formula, is given. It is also demonstrated that these surfaces coincide with those obtained from the Sym-Tafel formula. These two approaches correspond to parametrizations of one and the same surface in.