On $\pi_2$ Almost Geodesic Mappings of Almost Hermitian Manifolds

We consider a class of almost geodesic mappings, namely, almost geodesic mappings of class $\pi_2$, and obtain conditions under which almost Hermitian manifolds admit almost geodesic mappings of class $\pi_2$. We prove that an almost Hermitian manifold admits a $\pi_2$-mapping with respect to a Riemannian connection if and only if it is an $NK$-manifold. We obtain a condition on the defining form $\psi$ of any nontrivial $\pi_2(e)$-mapping under which a proper $NK$-structure is taken to a proper $NK$-structure.