Connection in a tangent bundle to the frame bundle of manifold
This paper focuses on the tangent bundle to the linear frame bundle of a smooth manifold. Brackets of the tangent vectors of this bundle are con-structed. A coordinate representation of the non-holonomic frame vectors is produced. Horizontal and vertical curvatures, torsions, and covariant ...
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 operator (a vertical vertical-valued form of 2nd order for 1st order affine connection) from 2nd order tangent space into 1st order tangent space to a manifold. It is shown that affine connection ...
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 of H’-lift given by ...
Eliseeva N. A., Popov Y. I.
... научных исследований Германа Федоровича Лаптева // Тр. геом. семинара. М., 1973. Т. 4. С. 7—70.
On constructions in Н(Λ, L)-distribution geometry of affin space
tensor, quasitensor, subbundle, bundle, linear polar, Bompiani—Pantazi correspondence, distribution, normalization, affine connection, central affine connection
5-17
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 внешних форм Картана и группы Ли. Чебоксары, 1997.
2. Столяров А. В. Системы уравнений Пфаффа ...
Bundles of Projective Normals of the Hyperband Distribution of an Affine Space
... -distribution for each L-, L-, H-subbundles generates three one-parametrical families of Norden internal normalizations in the 2nd order differential neighbourhood. Construction H-subbundle of the Fubini and Wilczynski projective normals is given. Canonical bundles of 1st and 2nd kind normals are constructed for each L-, L-, H-subbundles of the H-distribution.
1. Алшибая Э. Д. К геометрии распределений гиперплоскостных элементов в аффинном ...
Introduction of connections on a hypersurface ()
... (centroprojective) 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
Normal connections of the L-subbundle of a strongly mutual distribution of the projective space
... Mm Hn1, where r m n 1. This class is characterized by the fact that the pairs (, ), (L, ), (M, E) of the main structural subbundles of this threefold distribution are mutual. Invariant dual normal connections induced in bundles of the 1st and 2nd kind normals of the L-subbundle of this VH -distribution are examined.
1. Попов Ю. И. Сильно взаимные трехсоставные распределения проективного пространства ...
Fields of fundamental and captured geometrical objects of the 2nd or-der H-distribution of affine space
Norden inner normalization fields of basic structural Λ-, L-, H-sub-bundle of hyperband H-distribution are constructed in 2nd order differential neighborhood of affine space An by means of symmetric fundamental tensors of 1st order.
1. Попов Ю. И. Введение в теорию регулярного гиперполостного распреде-ления аффинного пространства // Вестник Балтийского федерального уни-верситета...
Linear and center-projective quotient groups of the second order differential group
... дифференциальной группы и структурные уравнения расслоения p-кореперов // Труды геометрического семинара. М., 1974. Т. 5. С. 239—257.
Kuleshov A.
jet, differential group, frame, bundle, center-projective group.
89-94
Fundamental-group connections, induced by composite clothing of family of centered planes in projective space
This paper continues the cycle of works dealing with connections on a smooth family of centered planes in projective space. It is shown that composite clothing of such a family induces three-parameter bunch of bundles of fundamental-group connections. One induced connection is allocated from each of this bundles. Coincidence conditions of the received connections and geometrical interpretation of the linear sub connections is given.
1. Белова О. О....