Invariant formulation of surfaces associated with CP^(N-1) models

In this paper, we provide an invariant formulation of completely integrable $CP^{N-1}$ Euclidean sigma models in two dimensions defined on the Riemann sphere $S^2$. The scaling invariance is explicitly taken into account by expressing all the equations in terms of projection operators. Properties of the projectors mapping onto one-dimensional subspaces are discussed in detail. The paper includes a discussion of surfaces connected with the $CP^{N-1}$ models and the wave functions of their linear spectral problem.