Akivis derivation formulas and Laptev structure equations on the surface of an affine space
The smooth surface in affine space is considered. With the derivation formulas and equations of the structure of an affine space constructed three pairs Akivis-Laptev on the surface. It is shown that the surface of an affine space is a holonomic smooth manifold.
1. Акивис М. А. Многомерная дифференциальная геометрия. Калинин, 1977.
2. Евтушик Л. Е. Уникальная школа Картана — Лаптева, ее сбережение ...
The derivation formulas and equations for an affine space structure from the point of view of smooth manifolds
... многообр. фигур. Калининград, 2015. Вып. 46. С. 168—177.
12. Josef Mikes et al. Differential geometry of special mappings. Olomouc, 2015.
13. Shevchenko Ju. I., Skrydlova E. V. About non-holonomicity of quotient manifold of holonomic distribution on semi-holonomic smooth manifold // Междун. конф. по алгебре, анализу и геометрии. Казань, 2016. С. 67—68.
Shevchenko Yu.
Akivis derivation formulas, Laptev structure equations, secondorder ...
Differential comparisons for the components of the curvature object of affine connection of the second order
... подмногообразия гладких многообразий // Диф. геом. многобр. фигур. Калининград, 2015. Вып. 46. С. 168—177.
Ryazanov N.
Laptev structure equations, affine connection, curvature object of the second order, holonomic smooth manifold, semi-holonomic smooth manifold, non-holonomic smooth manifold
23-29
Hierarchies of smooth manifolds up to zeroth and first orders
Hierarchies of smooth manifolds in the form of sequences are given. The sequence of zero order consists of the parallelized manifold, Lie group and Abelian group of Lie. Each of three sequences of the 1st order for the ho-lonomic, semi-holonomic and the non- holonomic smooth manifolds includes base of the parallelized bundle of linear coframes, in other words, base of space of expanded affine connection, base of space of affine connection torsion-free and affine space.
1. Лаптев Г. Ф. Основные ...
About geometrical objects fields of the -framed hypersurface of the projective space
The second-order curvature object contains the curvature object of the fundamental-group connection defined in the principal bundle; the curvature object of an affine connection over a manifold; second-order components. Differential comparisons for the components of the object of curvature of the second- order fundamental-group connection are made. These comparisons show that the curvature object forms a geometric object only in combination with components of the second-order connectivity object...
Strongly mutual threefold distributions of projective space
.... 117 151.
5. Лаптев Г. Ф. Дифференциальная геометрия погруженных многообразий. // Тр. моск. мат. об-ва. 1953. Т.2. С. 275 382.
Popov Yu.
distribution, nonholonomic tensor, holonomic distribution, hyperband, tensor, quasitensor, duality of distribution, adjoint surface system, quasinormal, subbundle.
62-67
Curvature of 2nd type induced on plane distribution
... the plane distribution is considered. The curvature of group connection of 2-nd type, induced by composite clothing of plane distribution, is constructed. It is proved, that a immovability of Cartan’s plane and Bortolotti’s hyperplane in case of holonomic distribution attracts the vanishing of curvature tensor of 2-nd type.
1. Лаптев Г. Ф., Остиану Н. М. Распределения m-мерных линейных элементов в пространстве проективной ...
Connection in a tangent bundle to the frame bundle of manifold
This paper focuses on the tangent bundle to the linear frame bundle of a smooth manifold. Brackets of the tangent vectors of this bundle are con-structed. A coordinate representation of the non-holonomic frame vectors is produced. Horizontal and vertical curvatures, torsions, and covariant derivatives are constructed in a homogeneous connection.
Бишоп Р., Криттенден Р. Геометрия многообразий. М., 1967.
2. Кобаяси Ш., Номидзу К. Основы...
Semiholonomical, holonomical and trivial spaces of affine connection
... n-dimensional space of affine connection An,n with Cartan’s structure equations Ricci’s and Bianchi’s identities were received. Their invariance has been shown. After prolongation of the structure equations using Laptev’s lemma semiholonomical, holonomical and trivial manifolds are defined. The Ricci’s identities allowed us to prove semiholonomicity of the space An,n. This semiholonomicity preserves in the space without torsion A’n,n and in the space without curvature ‘An,n , besides the ...
Introduction to a theory of regular hyperband distribution of an affine space
Regular hyperband distribution of an affine space (H-distribution) is given and its existence theorem is proved. Conditions of holonomic H-distribution is determined and Bompiani—Pantazi bijection between the first kind normal and the second one for associated with H-distribution H-, Λ- and L-subbundle is introduced.
1. Остиану Н. М. Распределение гиперплоскостных ...