Canonical Almost Geodesic Mappings of the First Type onto Generalized Ricci Symmetric Spaces

Abstract

In the paper we consider canonical almost geodesic mappings of spaces with
affine connection onto $m$-Ricci-symmetric spaces. In particular, we studied in detail canonical almost geodesic mappings of the first type of spaces with affine connections onto $2$- and $3$-Ricci-symmetric spaces. In either case the main equations for the mappings have been obtained as a closed mixed system of PDEs of Cauchy type. We have found the maximum number of essential parameters which the solution of the system depends~on.