Almost Geodesic Mappings of Spaces with Affine Connection

Special Almost Geodesic Mappings of the First Type of Non-symmetric Affine Connection Spaces

“…We extend results given in [4] to the case of affine connection spaces with torsion. We defined a special class of almost geodesic mappings of type π 1 of non-symmetric affine connection spaces π * 1 .…”

“…Generalizing the result of Berezovski and Mikeš [4], we introduce a special class of almost geodesic mappings of the first type of affine connection spaces with torsion. Also, we find some relations between curvature tensors of spaces with non-symmetric affine connections with respect to these mappings.…”

“…A lot of research papers and monographs are dedicated to the theory of conformal and geodesic mappings of Riemannian spaces, affine connected ones, and their generalizations. Sinyukov [19] and Mikeš [1][2][3][4][5][6]14,15,26] gave some significant contributions to the study of almost geodesic mappings of affine connected spaces, and they singled out three types π 1 , π 2 , π 3 of almost geodesic mappings between affine connected spaces without torsion.…”

On canonical F-planar mappings of spaces with affine connection

“…where ψ i (x), ϕ i (x) are components of linear forms ψ and ϕ. F-planar mapping is called canonical, if the form ψ in equation (2) vanishes. Evidently, F-planar mapping can be expressed as a composition of geodesic and canonical F-planar mappings.…”

“…Sinyukov [25], have recently been clarified in [12]. The next study of F-planar mappings is possible to find in [14] and also in [2,19]. In the paper [12], there was proved that PQ ε -equivalence, defined by P. Topalov, are previously studied F 2 -planar mappings.…”