Invariants of Immersions on n-Dimensional Affine Manifold
Djavvat KhadjievNational University of Uzbekistan named after Mirzo ULUGBEK, V.I. Romanovsky Institute of Mathematics, Uzbekistan Academy of Sciences,100125, Tashkent,UzbekistanGayrat BeshimovNational University of Uzbekistan named after Mirzo ULUGBEK, V.I. Romanovsky Institute of Mathematics, Uzbekistan Academy of Sciences,100125, Tashkent,Uzbekistanİdri̇s ÖrenKARADENİZ TEKNİK ÜNİVERSİTESİ
ABI
Аннотация
Main results: The system of Christoffel symbols of the connection of an immersion ξ:J→R^n of an n-dimensional manifold J in the n-dimensional linear space R^n is a system of generators of the differential field of all Aff(n)-invariant differential rational functions of ξ, where Aff(n) is the group of all affine transformations of R^n. A similar result have obtained for the subgroup SAff(n) of Aff(n) generated by all unimodular linear transformations and parallel translations of R^n. Rigidity and uniqueness theorems for immersions ξ:J→R^n in geometries of groups Aff(n) and SAff(n) were obtained. These theorems are given in terms of the affine connection and the volume form of immersions.
Темы
Идентификаторы
Цитирования и источники
Цитирований: 0Использованных источников: 16
Показатели — AkademScholar · Скоро