Results: **6**

#### 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

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 ...

#### 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** ...

#### 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

#### About horizontally vector lifts of tensor fields from the base to its tangent bundle

The vector field of the type , obtained fr om the tensor field on a **smooth** **manifold** M to the tangent bundle , arises in the study of infinitesimal affine transformations with a complete lift. The H-lift was introduced S. Tanno in 1974 in infinitesimal isometries on the tangent bundle with the complete lift. The definition ...

#### About geometrical objects fields of the -framed hypersurface of the projective space

... полуголономные подмногообразия гладких многообразий // Там же. 2015. Вып. 46. С. 168—177.
Popov Ju.
structure equations of Laptev; fundamental-group connection, the second order curvature object; semi-holonomic **smooth** **manifold**
16-23