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

(University of Nis, Serbia, 2022) Березовський, Володимир Євгенійович

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.
Geodesic mappings of affine-connected spaces onto Riemannian spaces

( 1992) Березовський, Володимир Євгенійович ; Berezovskii, V. E.

The paper deals with geodesic mappings of manifolds equipped with affine connections. The main result of the paper contains a local characterization of manifolds equipped with affine connections of zero torsion which admit geodesic mappings onto Riemannian manifolds (equipped with the Levy-Civita connection). The main source of results about geodesic mappings is the book of N. S. Sinyukov [Geodesic mappings of Riemannian spaces.