*Wojtek
J. ZAKRZEWSKI*

Department of Mathematical Sciences,

University of Durham,

Durham DH1 3LE UK

E-mail W.J.Zakrzewski@durham.ac.uk
*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.