On Canonical F-planar Mappings of Spaces with Affine Connection

Abstract

In this paper we study the theory of F-planar mappings of spaces with affne connection. We obtained condition, which preserved the curvature tensor. We also studied canonical F-planar mappings of space with affne connection onto symmetric spaces. In this case, the main equations have the partial differential Cauchy type form in covariant derivatives. We got the set of substantial real parameters on which depends the general solution of that PDE’s system.