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Information × Registration Number 0203U008083, 0100U003354 , R & D reports Title Geometry and topology of special classes of Riemannian mani folds popup.stage_title Head Borisenko O., Registration Date 22-04-2003 Organization Kharkov National University named after V.N.Karazin popup.description2 The investigation is to geometry of multi-dimensional Riemannian manifolds and submanifolds. We give the description of asymptotic behavior of ratio of total curvature of compact l- convex domains to the volume of their boundaries in Hadamard manifolds. A vector field on a given Riemannian manifold is considered as a submanifold id the tangent sphere bundlle with Sasaki metric and the condititions of their totally geodesic properties are found. We give a description of totally geodesic unit vector fields on 2-dimesional manifold of constant curvature. We propose a procedure for construction of spherical image of a curve in spherical and hyperbolic. We propose a procedure for construction of spherical image of a curve in spherical and hyperbolic space forms and prove the theorems analogous to ones proved by Weiner and Jacobi concerning the properties of spherical image of a closed curve in Euclidean space. We consider the submanifolds in Euclideanspace with flat normal connection having constant curvature of their Grassmann image. We give a complete description for the submanifolds of this kind. We classify, also, the points of 2- and 3- dimensional submanifolds in a complex. Euclidean space via the properties of their Grassmann image. We introduce a notion of h - convex polyhedron in a hyperbolic space and give a description of some properties of these objects. We use the methods of Riemannian geometry, geometry of manifolds and submanifolds, complex geometry and geometry of fiber bundles. The report contains the results of theoretical character. The results may be used in mathematical research in the field of differential geometry and modern theoretical physics, in teaching of modern Riemannian geometry for students of physical and mathematical faculties. Product Description popup.authors popup.nrat_date 2020-04-02 Close