On canonical almost geodesic mappings of the first type of affinely connected spaces (Q468068)

A curve of a space \(A_n\) with a torsion-free affine connection is called almost geodesic, if along the curve there exists a parallel field of two-dimensional planes containing the tangents of the curve. A mapping \(f: A_n\to \bar A_n\) is called almost geodesic, if it takes the geodesics (autoparallel curves) of \(A_n\) into almost geodesics of \(\bar A_n\). The authors find necessary and sufficient conditions in form of a mixed PDE system for \(f: A_n\to\bar A_n\) to be a partial case of a canonical almost geodesic mapping.