Results: **7**

#### The derivation formulas and equations for an affine space structure from the point of view of smooth **manifolds**

Using the derivation formulas of Akivis and the Laptev structure equations for smooth **manifolds**, two methods yield corresponding formulas and equations for an affine space are received. The hierarchy of smooth **manifolds** and a principal bundle of linear coframes over a smooth **manifold** are used.
1. Столяров А. В. Метод ...

#### Akivis derivation formulas and Laptev structure equations on the surface of an affine space

... 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 torsion tensor of an analog of the Neifeld connection on a Grass-mannian-like **manifold** of centered planes

This article considers the Grassmanian-like **manifold** of cen-tered m-planes in the projective space Pn. A torsion object of the Neifeld con-nection is introduced in the fibering over the **manifold** . It is shown that this object forms a tensor containing one elementary and four simple subtensors....

#### Parallel displacements of directions on the Grassmann-like **manifold** of centered planes

In projective space the Grassmann-like **manifold** of centered planes is considered. Parallel displacements of directions on this **manifold** are studied.
1. Белова О. О. Связность в расслоении, ассоциированном с грассманоподобным многообразием ...

#### 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 ...

#### Differential comparisons for the components of the curvature object of affine connection of the second order

... 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 ...