[en] A special class of the Euclidean two-dimensional SU(N+1) invariant chiral theory is studied. The field phi(x) takes its values in the most degenerated orbit of the abjoint representation of the group of G=SU(N). It is assumed that the space of the chiral field is the homogeneous space, i.e. the complex projective space of dimension, with the isotropy subgroup H. A generalization of the Belavin-Polyakov duality equations is given. The equations are shown to have solutions in the class of rational functions