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This research is motivated by similarity of basic equations of F-planar mappings of symmetric affine connection space AN involved by J. Mike and N. S. Sinyukov, and which have been studied by Mikes research group (I. Hinterleitner, P. Peška, J. Stránská) and almost geodesic mappings (specially almost geodesic mappings of the second type) of the space AN involved by N. S. Sinyukov and which have been studied by many authors. We used the formulas obtained by N. O. Vesic to obtain invariants for special F-planar mappings in this article. These invariants are analogous to invariants of geodesic mappings (the Thomas projective parameter and the Weyl projective tensor). [ABSTRACT FROM AUTHOR]

In this manuscript, the identities of Ricci Type with respect to a non-symmetric affine connection space are obtained and simplified. The components of commutation formulae are discussed. [ABSTRACT FROM AUTHOR]

Changes of curvature tensors of a non-symmetric affine connection space under the third type almost geodesic mappings of both the first and the second type are given in this paper. These curvature tensors are firstly presented as functions of a curvature tensor of the corresponding associated space. [ABSTRACT FROM AUTHOR]