A note on F-planar mappings of manifolds with non-symmetric linear connection

Following the basic facts of [Formula: see text]-planar mappings introduced by Mikeš and Sinyukov and further developed by Hinterleitner and Mikeš, we consider the notions of an [Formula: see text]-planar curve and an [Formula: see text]-planar mapping, but in case of manifolds endowed with a non-symmetric linear connection and an affinor structure. Consequently, we investigate infinitesimal [Formula: see text]-planar and particularly geodesic transformations of manifolds with non-symmetric linear connection and find necessary and sufficient conditions for the existence of these transformations.

On almost geodesic mappings of the second type between manifolds with non-symmetric linear connection

We derive two mixed systems of Cauchy type in covariant derivatives of the first and second kind that ensures the existence of almost geodesic mappings of the second type between manifolds with non-symmetric linear connection. Also, we consider a particular class of these mappings determined by the condition ?F = 0, where ? is the symmetric part of non-symmetric linear connection ?1 and F is the affinor structure. The same special class of almost geodesic mappings of the second type between generalized Riemannian spaces was recently considered in the paper (M.Z. Petrovic, Special almost geodesic mappings of the second type between generalized Riemannian spaces, Bull. Malays. Math. Sci. Soc. (2), DOI :10.1007/s40840-017-0509-5)