On canonical almost geodesic mappings of the first type of affinely connected spaces

In this paper, we study special cases of canonical almost geodesic mappings of the first type of affinely connected spacešThe basic equations of mappings in question are reduced to a closed system of Cauchy type in covariant derivatives, and the number of essential parameters in the general solution of this system is estimated. We give an example of such mappings from a flat space onto another flat space. The mappings constructed send straight lines of the first space into parabolas in the second space. These almost geodesic mappings of the first type do not belong to the classes of mappings of the second and third types.