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On canonical F-planar mappings of spaces with affine connection

In this paper we study the theory of F-planar mappings of spaces with affine
 connection. We obtained condition, which preserved the curvature tensor. We
 also studied canonical F-planar mappings of space with affine 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.