Registration Number
0214U007986,
0113U003271
, R & D reports
Title
The geometry and topology of manifolds and submanifolds in Riemannian and Finslerian spaces
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Head
Yampolsky Aleksandr, Доктор фізико-математичних наук
Registration Date
19-01-2015
Organization
Kharkov National University named after V.N. Karazin
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Actual problems of modern geometry of submanifolds were considered. The conditions under which a hypersurface with limited normal curvature is contained in some layer were established. Isoperimetric inequalities for such hypersurfaces were obtained. Totally geodesic unit cross sections in bundles endowed with Sasaki metric and geodesics of Berger-deformed Sasaki metric were investigated. The conditions for stability of different classes of minimal submanifolds in Lie groups were obtained. The asymptotic estimates for curvatures of hyperspheres in the Hilbert geometry were proved. Submanifolds in an affine space with the degenerate affine fundamental form were studied. The problem of restoring ruled surfaces from their Grassmann image was solved.
Product Description
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Борисенко О.А.
Горькавий В.О.
Драч К.Д.
Олін Є.А.
Петров Є.В.
Шугайло О.О.
Ямпольський О.Л.
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2020-04-02
