2F-планарні відображення псевдоріманових просторів з f-структурою

Abstract

Article is devoted to a problem of diffeomorphisms of the manifolds with affinor structure of some type. The concept of 2F-planar mapping of spaces with a‑ne connection and Riemannian spaces was deneded by R. J. Kadem. It is natural generalization of F-planar mappings and includes as a special case such known diffeomorphisms of the spaces with affine connection and Riemannian spaces with affinor structure as geodesic, quasi-geodesic, holomorphically projective mappings. R. J. Kadem investigated the common questions of the theory of 2F-planar mappings of the spaces with affine connection and Riemannian spaces with affinor structure. In particular, he proved that such mapping as necessary preserves affinor structure. Kurbatova I.N. studied 2F-planar mappings of pseudo-Riemannian spaces with the third order affinor structure F, which is given by the equation . Konovenko N.G. considered some questions of 2Fplanar mappings of pseudo-Riemannian spaces with covariantly constant f-structure F which is given by the equation . In the present article the research of 2F-planar mappings of Pseudo-Riemannian spaces with f-structure continues. It is proved that the Pseudo-Riemannian space with covariantly constant f-structure represents a direct product of pseudo-Riemannian spaces, one of which admits Kahlerian structure; the class of pseudo-Riemannian spaces with covariantly constant f-structure is closed concerning the considered mappings; on condition of covariant constancy of an affinor of f-structure 2F-planar mappings can be one of three types: the complete and canonical of I, II type; depending on type 2F-planar mapping induces geodesic, holomorphically projective or affine mapping on components of the product of the displayed spaces. In the theory of diffeomorphisms of manifolds wide classes of the Riemannian spaces admiting geodesic mappings and the Kahlerian spaces admiting holomorphically projective mappings which preserve complex structure are known. Therefore results of article give the chance to construct numerous classes of pseudo-Riemannian spaces with absolutely parallel f-structure and their 2F-planar mappings.