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

Abstract

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 $\nabla F=0$, where $\nabla$ is the symmetric part of non-symmetric linear connection $\underset1\nabla$ 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 \big(M.Z. Petrovi\'c, {\it Special almost geodesic mappings of the second type between
generalized Riemannian spaces}, Bull. Malays. Math. Sci. Soc. (2), \texttt{DOI :10.1007/s40840-017-0509-5}\big).