CP^N-1  harmonic maps and the Weierstrass problem

Abstract:
A Weierstrass-like system of equations corresponding to the CP^N-1 harmonic maps is presented. The system constitutes a further generalisation of our previous construction. It consists of four first order equations for three complex functions which are shown to be equivalent to the CP^N-1 harmonic maps. When the harmonic maps are holomorphic (or antiholomorphic) one of the functions vanishes and the system reduces to the previously given generalisation of the Weierstrass problem.
We also discuss a possible interpretation of our results and show that in our new case the induced metric is proportional to the total energy of the map and not only to its holomorphic part, as was the case in the previous generalisations.