Abstract
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 determine post- Riemannian geometries and almost Hermitian connections in the class W4. We examine conformal transformations of almost Hermitian structures and affine mappings of connections generated by these transformation and find connections invariant under these mappings.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 180, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 2, 2020.
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Gorginyan, Y.A., Ignatochkina, L.A. Space of Affine Connections of an Almost Hermitian Manifold. J Math Sci 276, 498–507 (2023). https://doi.org/10.1007/s10958-023-06770-x
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DOI: https://doi.org/10.1007/s10958-023-06770-x