Geodesic
Examples of affine-metric structures on an almost Hermitian manifold
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 30-40

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On an almost Hermitian manifold, we construct an affine subspace of affine connections by using the covariant differential of the almost complex structure on the Riemannian connection of a pseudo-Riemannian metric. We find possible dimensions of this space. For the $8$-dimensional space, we find multidimensional planes of connections that determine post-Riemannian geometries. We also find connections for which the torsion tensor is determined only by the structural tensor or only by the virtual tensor. We fond connections in which the covariant differential of the almost complex structure is determined only by the structural tensor or only by the virtual tensor.
Keywords: affine connection, almost Hermitian manifold
Mots-clés : conformal transformation. 
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     author = {L. A. Ignatochkina and Yu. A. Gorginyan},
     title = {Examples of affine-metric structures on an almost {Hermitian} manifold},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {30--40},
     publisher = {mathdoc},
     volume = {181},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_181_a4/}
}
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L. A. Ignatochkina; Yu. A. Gorginyan. Examples of affine-metric structures on an almost Hermitian manifold. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 30-40. http://geodesic.mathdoc.fr/item/INTO_2020_181_a4/