Geodesic
The space of affine connections of 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 2, Tome 180 (2020), pp. 31-40

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We consider affine connections determined by an almost Hermitian structure of a smooth manifold. We prove that the affine space of connections considered has dimension $12$ if and only if the Lie form of the almost Hermitian structure is nonzero. We find connections that define post-Riemannian geometries and almost Hermitian connections in the class $W_4$. We examine a conformal transformation of an almost Hermitian structure and an affine mapping of connections generated by this transformation and find a connection invariant under this mapping.
Keywords: affine connection, almost Hermitian manifold
Mots-clés : conformal transformation. 
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     author = {Yu. A. Gorginyan and L. A. Ignatochkina},
     title = {The space of affine connections of 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 = {31--40},
     publisher = {mathdoc},
     volume = {180},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_180_a4/}
}
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Yu. A. Gorginyan; L. A. Ignatochkina. The space of affine connections of 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 2, Tome 180 (2020), pp. 31-40. http://geodesic.mathdoc.fr/item/INTO_2020_180_a4/