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Abstract
The article studies 2F-planar mappings of pseudo-Riemannian spaces equipped with a certain type of affinor structure. The concept of a 2F-planar mapping of affine-connected and Riemannian spaces was introduced by R.J. Cadem. In his works, the general questions of the theory of 2F-planar mappings of affine-connected and Riemannian spaces equipped with an affinor structure were investigated. In particular, he proved that such a mapping, of necessity, preserves the affinor structure. We consider a 2F-planar mapping of pseudo-Riemannian spaces with an absolutely parallel f-structure. Earlier, we proved that a pseudo-Riemannian space with an absolutely parallel f-structure is a product of two pseudo-Riemannian spaces, one of which is Kahler; the class of pseudo-Riemannian spaces with an absolutely parallel f-structure is closed with respect to the mappings under consideration; under the condition of covariant constancy of the affinor, the f-structures in the displayed spaces, non-trivial 2F-planar mappings can be of three types: full and canonical I, II types; depending on the type, the 2F-planar mapping induces a geodesic, holomorphically-projective or affine mapping on the components of the product of the displayed spaces.
This article continues the study of 2F-planar mapping of pseudo-Riemannian spaces with absolutely parallel f-structure. For all types of this mapping (main and canonical I and II), geometric objects are constructed that are invariant with respect to the mappings under consideration: an inhomogeneous object (such as the Thomas parameters in the theory of geodesic mappings of Riemannian spaces) and a tensor (of the holomorphically projective curvature tensor type in the theory of holomorphically- projective mappings Kahler manifolds). Classes of spaces (2F-flat, 2F (I) - and 2F (II) -flat), admitting 2F-planar mapping, are distinguished. For them, the structure of the Riemann tensor is revealed and analogues of the Beltrami theorem from the theory of geodesic mappings are proved. The metrics of 2F-, 2F (I) - and 2F (II) -flat spaces in a special coordinate system are found.
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