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Information × Registration Number 0305U003240, 0103U004232 , R & D reports Title Extinsic geometry of multidimensinal submanifolds popup.stage_title Дослідження властивостей підмноговидів у гіперболічних просторових формах Head Borisenko A, Registration Date 02-03-2005 Organization Kharkov national university named after V.N. Karazin popup.description2 An object of the research is submanifolds in Riemannian manifolds with specific geometrical properties. Be considered submanifolds generated by the unit vector fields on Riemannian manifolds. Were considered the relating questions of the manifolds' geometry, and that can be applied to the study of the geometry of vector fields. An aim of this work is the research of interconnection between geometrical characteristics of manifolds and its submanifolds. In particular, the vector fields are considered as a submanifolds in the unit tangent bundle of the manifold. We study Chern-Lashof total curvature of complex submanifolds, minimal ruled surfaces in some three-dimensional Riemannian space, affine immersions. Methods of the research - Riemannian geometry, geometry of submanifolds, geometry of fiber spaces, complex analysis, methods of theory garmonic maps, affine geometry. It was given a full description of totally geodesic unit vector fields on two-dimensional manifold, it was found the connection between Chern-Lashof's total curvature and the volume of Grassmanian image of submanifold, it was given a description of ruled surfaces in the Geizenberg group, it was studied the conditions of univalent determination, the complex submanifolds according to Grassmanian image, it was found the approaches to classification of the flat affine submanifolds of arbitrary ko-dimension. Product Description popup.authors popup.nrat_date 2020-04-02 Close