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Information × Registration Number 0217U000173, 0111U010461 , R & D reports Title Development of the theory of invariant types of diffeomorphisms and the elements of proper theory of tangent bundles. popup.stage_title Head Sinukova Elena, Registration Date 23-01-2017 Organization South Ukranian State Pedagogical University named after K.D. Ushynskyy popup.description2 Object of research (study): the different types of geometric diffeomorphisms, in particular, automorphisms, geometry of tangent bundle. Purpose: to study the peculiarities of technique of using singular integral equations for solving some special mathematical physics problems; to conduct investigation of properties of some types of finite groups, in particular, of some finite groups of transformations. Methods of research: theoretical; logical-system, comparative analysis, classification, analogy, induction, deduction, computer modeling. Theoretical and practical results: The series of type of uniquely definiteness in a whole theorems about geodesic mappings of Riemannian spaces , that satisfy defined conditions of differential-algebraic character, series of type of uniquely definiteness in a whole theorems about holomorphically-progective mappings of Kahler spaces, that satisfy some special conditions of differential-algebraic character, have been obtained. The coefficients of the series depend not only on coordinates of the current point but also on components of tangent vector in it. If in corresponding series for components of metric tensor and for components of object of affine connection we neglect, accordingly, the addends of the third, the second and higher order of smallness relative to the components of tangent vector, we obtain components of affine connection and components of metric tensor that define on the base space geometry, that is similar to Finsler' geometry, but, in contrast to it, is in a natural way connected with the invariant theory of approximations in Riemannian spaces. The rule of complete lift ensures an opportunity of building different geometries of tangent bundle. Investigation of such geometries has been started. Almost geodesic mappings of the first and the second types of affine connected spaces with torsion have been investigated. We have studied the internal peculiarities of almost Hermitian spaces. After this geodesic mappings and transformations of such spaces are considered. Novelty, efficiency of introduction: All results, that have been obtained, are the new actuality. The next results of its approval testify the fact: the reports on international conferences, the published articles. Field (domain) of application: Mathematics, theoretical physics. Product Description popup.authors Драганюк С. В. Зернов О. Є. Ладиненеко Л. П. Яковлева О.М. popup.nrat_date 2020-04-02 Close