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Information × Registration Number 0212U005173, 0107U000947 , R & D reports Title Geometric and topologic properties "in large" of surfaces and Riemannian spaces with curvature of constant and varied sign and their applications popup.stage_title Head Aminov Yuriy Akhmetovich, Registration Date 28-03-2012 Organization B.Verkin Institute for Low Temperature Physics and Engineering of National Academy of Science of Ukraine popup.description2 Theorems on the stability of minimal submanifolds in Riemannian spaces are proved. A problem conserning the recosntruction of an explicit submanifold of Euclidean space fromits Grassmann image is solved. A multi-dimensional analogue of the Hylbert theorem, which states the non-existence of isometric immersions of the Lobachevsky space into the Euclidean space under additional assumption of flat normal connection and bouded mean curvature, is proved. Geometric properties of pseudo-spherical Rozendorn surface are studied. Theorems on the existence of geometric properties of Bianchi-Backlund type for pseudo-spherical surfaces in constant curvature spaces and in product spaces are proved. Many-dimensional pseudo-spherical submanifolds with Bianchi transformation degenerated into line are described. The existence ofpolynomial solutions for the Monge-Ampere equation with quadratic right hand side is studied. A geometric representation for minimal light-like surfaces in the Minkowski space is derived. Orientable three-dimensional manifolds addmittin foliations of non-negative curvature are classified. The contractibility of the universal covering of a manifold endowed with a foliation with uniformly contractible universal covering of sheets. A geometric estimate for the number of homotopic classes of tangent distribution on the two-dimensional torus is found. The existence of hyperbolic or parabolic) foliation on an arbitrary closed oriented three-dimensional manifold is shon. An uniformization theorem for contact structures on three-dimensional manifolds is proved. The Gromov conjecture about the macroscopic dimension of the universal covering is proved in the case of compact spin-manifolds with positive scalar curvature satisfying additional assumptions. Group properties of antipodal polygons, which are relied to the problemof inscribing a multy-dimensional simplex into acube of the same dimension, are discovered and studied. D. Bleecker results on the possibility to increase the voume of right polyhedra with the help of linear bendings are sharpened. An optimization problem for the form of a strongly convex shell with boundary under an extrinsic pressure is formulated and studied. New applications of the surface theory are presented for describe the beam of charged particles in a constant magnetic field as well as wave functions of elementary particles. Product Description popup.authors Бабенко В.І. Болотов Д.В. Горькавий В.О. Мілка А.Д. Медяник А.Г. popup.nrat_date 2020-04-02 Close