On the Equations of Conformally-Projective Harmonic Mappings

In this paper we study compositions of conformal and geodesic diffeomorphisms, which are at the same time harmonic mappings (conformally‐projective harmonic mappings). The equations of conformally‐projective harmonic mappings are shown. We obtained the fundamental equations of these mappings in form of a system of differential equations of Cauchy type. Solutions of this system depend on at most 12(n+1)(n+2)−(n−2) independent parameters.