On the Equations of Conformally-Projective Harmonic Mappings

Abstract

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 1 2 (n + 1)(n + 2) − (n − 2) independent parameters.

Geodesic mappings and differentiability of metrics, affine and projective connections

“…To theory of geodetic mappings and transformations were devoted many papers, these results are formulated in large number of researchs and monographs [1], [2], [3], [4], [5], [7], [8], [9], [10], [11], [12], [13], [14], [16], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [30], [31], [32], [33], [34], [35], [36], [37], etc.…”

On global geodesic mappings of $n$-dimensional surfaces of revolution

“…Geodesic mappings of equidistant spaces were studied by N.S. Sinyukov [22,23] and, in the following, by many other authors, for example [4,5,6,11,12,13,14,15,16,17,18,19,20,21,26].…”