On canonical 2F-planar mappings of the first type of pseudo-Riemannian spaces with f-structure

Abstract

The article is devoted to the basic questions of the theory of 2F-planar mappings of manifolds, which are endowed with a certain type affinor structure. We proved that the class of pseudo-Riemannian spaces with absolutely parallel f-structure is closed with respect to the considered mappings. In addition, under the condition of covariant constancy of the affinor f-structure in the mapped spaces, non-trivial 2F-planar mappings can be of three types: complete and canonical of types I and II. Previously, we studied complete 2F-planar mappings in detail. This article considers the main issues for canonical 2F-planar mappings of the first type. Theorems have been proved that give a regular method that allows for any pseudo-Riemannian space with absolutely parallel f-structure (V_n, g_ij, F^h_i) to either find all spaces (V'_n, g'_ij, F'^h_i) onto which V_n admits a canonical 2F-planar mapping of the first type, or to prove that there are no such spaces. In particular, we have shown that a pseudo-Riemannian space with absolutely parallel f-structure, in which there is a concircular or quasi-concircular vector field, admits a non-trivial canonical 2F-planar mapping of the first type.