INTRODUCTION

Smith showed in example 8.13(S1) that his methods to construct harmonic maps between Euclidian spheres definitely fall to give a harmonic representative of homotopy classes in μ₃(s²) corresponding to hoof invariant KL whit K≠L.

            The aim of this paper is to solve the rendering problem for μ₃ (s²), i.e. to prove that μ₃ (s²) can be represented by harmonic maps provided that the domain is deformed by using a suitable Riemannian metric. We also make a few comments on the physical meaning of the deformation and on the energy of our maps.

RESUMEN

            In this paper we extend some properties of analytic functions on several complex variables to solution of overdeterminated systems of complex partial differential equations. It is proved that many global properties of analytic functions are true for solutions of the Vekua system in special cases. The relation between analytic functions and solutions of quasi-linear systems is discussed in the paper.