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 ...
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 ...
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 ...
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....
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
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 ...
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
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.
jet, differential group, frame, bundle, center-projective group.
Hierarchies of smooth manifolds up to zeroth and first orders
... 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 manifolds includes base of the parallelized bundle of linear coframes, in other words, base of space of expanded affine connection, base of space of affine connection torsion-free and affine space.
1. Лаптев Г. Ф. Основные инфинитезимальные структуры ...
Practical physics lessons based on PC interfaced ADC-DAC module
... of analog-to-digital and digital- to-analog converter (ADC-DAC) at practical physics lessons in a college. The authors analyze prepared laboratory class materials in Physics, based on reasonably priced Russian-manufactured «ZET-210» DAC-ADC module. Bundled ZETLAB software enables to turn a computer into a physics minilaboratory, which allows to generate, measure, analyze signals, and visualize measurements. The article demonstrates sure advantages of the use of DACADC technology base at practical ...
About geometrical objects fields of the -framed hypersurface of the projective space
The second-order curvature object contains the curvature object of the fundamental-group connection defined in the principal bundle; the curvature object of an affine connection over a manifold; second-order components. Differential comparisons for the components of the object of curvature of the second- order fundamental-group connection are made. These comparisons show that ...
About generalizations of the Cartan projective connection on smooth manifold
... connection from which canonical connection is marked out. The Cartan projective connection and its canonical version are obtained from a projectivity condition. On the other hand, the projective structure is presented in the form of the principal fiber bundle of the special center-linear coframes. The giving fundamental- group connection in this fibering is made by means of the center-linear connection object, not coinciding with the previous objects of connections.
1. Лаптев Г. Ф. Основные ...
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 ...