Giving the 1st order affine connection by means of the 2nd order vector-valued forms
Affine connection is given by 2nd order vectors called horizontal. Vertical and horizontal forms of 2nd order are entered for 1st order affine connection. It is proved that symmetric affine connection in the bundle of tangent linear frames defines vertical linear ...
Semiholonomical, holonomical and trivial spaces of affine connection
In 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 ...
Normal generalized affine connection associated with the Grassman-like manifold of centred planes
In projective space a Grassman-like manifold of centred planes is considered. The normal affine connection, associated with the manifold, is set in generalized fibering. Field of the affine connection object defines torsion and curvature tensors contained one elementary and one simple subtensor every. A canonical case of normal generalized affine ...
Eliseeva N. A., Popov Y. I.
The authors construct Foss and Green's normalizations in Norden's sense internally invariantly. The research sets tangent affine connections and tangent central affine connections of the main structural subbundles of H(L, L)-distribution of affine space.
1. Попов Ю. И. Нормализация основных структурных подрасслоений H(L, L)-распределения ...
A Grouped Hyperplane Distribution of an Affine Space
... distribution of the affine space An (SH-distribution) and prove the relevant existence theorem. I perform internal normalizations of the main structural subbundles of the SH-distribution in first and second-order differential neighbourhoods. Normal and tangent affine connections of the main structural subbundles of the SH-distribution are introduced.
1. Попов Ю. И. О проективно-дифференциальной геометрии двухсоставного гиперполосного распределения ...
Hierarchies of smooth manifolds up to zeroth and first orders
... 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 инфинитезимальные структуры высших поряд-ков на гладком многообразии ...
Akivis derivation formulas and Laptev structure equations on the surface of an affine space
... 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 ... ... многообразий. Калининград, 1998.
6. Catuogno P. On stochastic parallel transport and prolongation of connections // Revista de la Unión Mathemática Argentina. 1999. Vol. 41, № 3. P. 107–118.
7. Emery M. An invitation to second-order ...
A semicanonical normal affine connection associated with the distribution
In manydimensional projective space distribution of planes is considered. The way of giving normal generalized affine connection associated with the distribution is proposed. It is shown that this connection is given by connection tensor and normal linear connection object. They define its curvature and torsion tensors. Semicanonical case is investigated when subtensor ...
Introduction of connections on a hypersurface ()
... connections on normalized (Norden’s framed) hypersurface n-1() Pn in its various subbundles. Coverages of the corresponding curvature 2 forms and curvature tensors of its connections are given.
Popov Yu. I.
normalization, bundle, subbundle, affine connection, centrorojective connection (normal connection), curvature 2 form, curvature tensors of connection
Differential comparisons for the components of the curvature object of affine connection of the second order
Differential comparisons for the components of the curvature object of affine connection of the second order are received. These comparisons show that, in the general case, the second-order curvature object forms a geometric object only in conjunction with the first-order curvature object and the second-order connectivity object....
The derivation formulas and equations for an affine space structure from the point of view of smooth manifolds
... конф. по алгебре, анализу и геометрии. Казань, 2016. С. 67—68.
Akivis derivation formulas, Laptev structure equations, secondorder vectors, semi-holonomic smooth manifold, bundle or linear coframes, affine connection
About fields of geometrical objects connected with the complex central nondegenerate hyperquadrics
A field of some geometrical objects internally connected with a complex (n-parametrical family) of the central nondegenerate hyperquadrics in n-dimensional affine space are defined and their geometrical sense is found out.
1. Кретов М. В. Дифференцируемые многообразия, ассоциированные с комплексами центральных невырожденных ...
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 ...