Geodesic
On $\pi_2$ Almost Geodesic Mappings of Almost Hermitian Manifolds
Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 517-526

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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.
Keywords: almost Hermitian manifold, nearly Kählerian ($NK$)-manifold, almost geodesic mapping, affine connection, Riemannian connection, pseudo-Riemannian manifold. 
@article{MZM_2011_90_4_a2,
     author = {A. V. Emelianov and V. F. Kirichenko},
     title = {On $\pi_2$ {Almost} {Geodesic} {Mappings} of {Almost} {Hermitian} {Manifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {517--526},
     publisher = {mathdoc},
     volume = {90},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a2/}
}
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A. V. Emelianov; V. F. Kirichenko. On $\pi_2$ Almost Geodesic Mappings of Almost Hermitian Manifolds. Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 517-526. http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a2/