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Information × Registration Number 0207U000931, 0104U003033 , R & D reports Title Geometry "in large" and topology of Riemanniann spaces and submanifolds popup.stage_title Head Aminov Yuriy Akhmetovich, Registration Date 15-02-2007 Organization B.Verkin Institute for Low Temperature Physics and Engineering of National Academy of Science of Ukraine popup.description2 A new formula for the Gauss torsion of an implicit surface in four-dimensional euclidean space is obtained. Precise estimates are found for the size of a domain in Euclidean space E^2n-1 which may admit a regular coordinate system of Bianchi. Bianchi transformations for pseudo-spherical surfaces in four-dimensional Euclidean space E^4 are described. The existence of pseudo-spherical surfaces in E^4 with hyperbolic, elliptic or parabolic Gauss image is proved. Conformal deformations of surfaces in Minkowski space M^n are described, which preserve the Gauss image. The problem is solved about the existence of contact structures on compact Threedimensional Riemannian manifolds, generated by the factorization of classical Thurston geometries. For compact Riemannian manifolds with dimension n>3, a conjecture of Gromov about macroscopic dimension is solved in negative. New theorems are demonstrated about the possibility to inscribe a right multi-dimensional symplex into a cube of the same dimension.5635 Product Description popup.authors popup.nrat_date 2020-04-02 Close