Local theory of solutions for the 0(2k + 1)sigma-model

We develop a theory of solutions n for the Euclidean nonlinear 0(2k + 1)sigma-model for arbitrary k and for a region G contains IR2. We consider a subclass of solutions characterized by a condition which is fulfilled, for G = IR2, by those n that live on the Riemann sphere S2 is contained in IR2. We are able to characterize this class completely in terms of k meromorphic functions, and we give an explicit inductive procedure which allows us to calculate all 0(2k + 1) solutions from the trivial 0(1) solutions. (orig.)