Regularities of the theory of quasi-geodesic mappings of special parabolic spaces

We study quasi-geodesic mappings (QGM) of generalized-recurrent-parabolic spaces f: (Vn, gij, Fih) → (V'n, g'ij, Fih). QGM can be of two types: general and canonical. This article examines the QGM of the general type. Earlier, we considered the fundamental questions of the theory of QGM of generalized-recurrent-parabolic spaces. We proved theorems that allow for any generalized-recurrent-parabolic space (Vn, gij, Fih) to either find all spaces (V'n, g'_{ij}, Fih) on which Vn admits QGM of the general form, or prove that there are no such spaces. In this article, we constructed a Γ-transformation that makes it possible to obtain from a pair of generalized-recurrent-parabolic spaces that are in a quasi-geodesic mapping, an infinite sequence of pairs of other generalized-recurrent-parabolic spaces, which are also in a quasi-geodesic mapping.