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Information × Registration Number 0209U006038, 0106U001538 , R & D reports Title Geometry of manifolds and submanifolds popup.stage_title Head Borisenko A, Registration Date 19-01-2009 Organization Kharkov National University named after V.N.Karazin popup.description2 The main objects of the research are Lie groups, Finsler-Hadamard manifolds, complex Grassmann manifolds and submanifolds in the unit tangent bundle of a Riemannian manifold. The topics cover the isometric immersions of Nil-manifolds into Euclidean space, hypersurfaces in Finsler-Hadamard spaces, harmonicity of Grassmann image of a submanifold in Heisenberg group, extremal values for holomorphic curvature of complex Grassmann manifold, unitl vector fields as submanifolds in the unit tangent bundle, special spline -approximations. The goal of the research is studying the interrelations between geometrical characteristics of the manifold and its submanifold. The results include the isometric non-immersability of the certain classes of Lie groups into Euclidean space of corresponding dimension, the Finslerian analogues of some comparison theorems from Riemannian geometry, the expression for holomorphic curvature of complex Grassmann manifold via singular numbers numbers, the stability / instability of unit totally geodesic vector fields on two-dimensional manifold, the new way for representation polynomial splines for modelling of irregular manifold. NIL-MANIFOLD, FINSLER-HADAMARD MANIFOLD, COMPLEX GRASSMANN IMAGE, SASAKI METRIC, HARMONIC MAPPING, POLYNOMIAL SPLINE. Product Description popup.authors popup.nrat_date 2020-04-02 Close