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Information × Registration Number 0207U008304, 0107U011249 , R & D reports Title Geometry and topology of multydimensional submanifolds popup.stage_title Head Leybina O, Registration Date 06-12-2007 Organization Kharkov National University named after V.N.Karazin popup.description2 The main objects of the research are the submanifolds in Riemannian and Finsler manifolds with definite geometrical properties. The main goal is to study the geometrical and topological properties of the multidimensional submanifolds. The principal methods of the study are the methods from the Riemannian geometry, the Finsler geometry, geometry of submanifolds, algebraic topology, the Morse theory , Lie groups theory. The project is based on modern achievements in the field of geometry and topology. The main of them are: extrinsic geometry of complex submanifolds in a complex Euclidean space and geometrical properties of Grassmann image of complex submanifolds; geometry of submanifolds in nilpotent Lie groups with left invariant metric; geometry of convex hypersurfaces in a Finsler-Hadamard manifolds; topology of saddle submanifolds in Riemannian spaces. Key words:Complex submanifolds, Grassmann image, Grassmann manifolds, Holomorphic curvature, Nilpotent Lie groups, Left invariant metric, Gauss map, Finsler geometry, Finsler-Hadamard manifolds, Homotopic groups Product Description popup.authors popup.nrat_date 2020-04-02 Close