On analytic descriptions of two-dimensional surfaces associated with the CP^(N-1) sigma model

Abstract

We study analytic descriptions of conformal immersions of the Riemann sphere S^2 into the CP^(N-1) sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is given. It is also demonstrated that these surfaces coincide with the ones obtained from the Sym-Tafel formula. These two approaches correspond to parametrizations of one and the same surface in R^(N^2-1).