Results: **10**

#### 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 ...

#### 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 ...

#### 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** ...

#### 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 ...

#### 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....

#### 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**
18-24

#### 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.
Shevchenko Yu.
Akivis derivation formulas, Laptev structure equations, secondorder vectors, semi-holonomic smooth manifold, bundle or linear coframes, **affine** **connection**
5-13

#### 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 ...