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 ...