Classical solutions of [formula omitted]P n non linear σ -models; an algebraic geometrical description

Abstract

The classical SO (3)-invariant σ-model and its suitably generalized versions are studied from the geometrical point of view. Known mathematical results concerning harmonic and holomorphic maps of a Riemann surface into the n-dimensional complex projective space are briefly reviewed. These are used to give a classification of classical solutions (both instantons and a certain subclass of unstable solutions) of C P n models and to study the properties of their energy spectrum.