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Information × Registration Number 0217U002475, 0112U002641 , R & D reports Title Geometry "in large" of Riemannian ans semi-Riemannian spaces and its applications to physics and mechanics popup.stage_title Head Aminov Yu.A., Registration Date 20-02-2017 Organization B.Verkin Institute for Low Temperature Physics and Engineering NAS of Ukraine popup.description2 New theorems are proved concerning the reduction of codimension for submanifolds of Euclidean and spherical spaces. The Hopf conjecture is proved for a wide class of metrics on product of two-dimensional spheres. New theorems are proved concerning polynomial solutions of the Monge-Ampere equation. Gromov conjectures concerning the reduction of the macroscopic dimension of closed manifolds are proved for the particular case of totally non-spin manifolds. The Stak conjecture concerning the existence of codimension one foliations of non-negative curvature in manydimensional spheres is completely solved. A criterion of planarity for codimension one foliations of non-negative curvature is proved. A problem settled by Y. Zelinsly on the existence of 2-convex embedding of two-dimensional sphere into four-dimensional Euclidean space is solved in the smooth case. Pseudo=sopherical surfaces, which admit Bianchi transformations, in four-dimensional spherical and hyperbolical spaces are described. A multidimensional syntetic generalization of The Baecklund transformation of pseudo-spherical syrfaces is proposed. New methods using the theory of polyhedra to the studying of the kernel structure are proposed. New estimates for the Gaussian curvature of closed surfaces are derived and applied in the thory os shells for finding asymptotics of critical loads of convex shells with restrictions on shells sizes. An analog of the Barker-Larman problem is solved for convex polygons in the hyperbolic plane. In 3d-theory of elsticity axe-symmetric non-linear deformations of gently sloping rigidly fixed shells under uniform extrinsic pressure are analysed. Product Description popup.authors Амінов Ю.А. Бабенко В.І. Болотов Д.В. Горькавий В.О. Гурін О.М. Калінін Д.С. Костенко О.В. Мілка А.Д. Медяник А.Г. Наседкіна Я.С. Невмержицька О.М. popup.nrat_date 2020-04-02 Close