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