Harmonic mappings of two-dimentional fields connected to 2-family of planes in E4 invariantly

Two-dimentional manifold V-2.2(1) of planes L-2(1) is studied in four-dimensional Euclidean space E-4. The two-dimentional manifold V-2.2(2) associates with this manifold. The planes are, orthogonal to the appropriate planes L-2(1) of the points A and equipping planes of manifold V-2.2(1). There are mappings between the appropriate planes L-2(1) and L-2(2) is an element of V-2.2(2). The geometrical sense of these displays is found out Particular cases are found out, when the given mappings satisfy to either Cauchy-Riernann or d'AlambertEuler conditions or they Are harmonious in some or all points of the corresponding planes L-2(1) or L-2(2). All considerations have local character, and the mappings are assumed analytical.