
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 Hlift 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 constructed. A coordinate representation of the nonholonomic frame vectors is produced. Horizontal and vertical curvatures, torsions, and covariant ...

Giving the 1st order affine connection by means of the 2nd order vectorvalued 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 verticalvalued 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, Hsubbundles generates three oneparametrical families of Norden internal normalizations in the 2nd order differential neighbourhood. Construction Hsubbundle of the Fubini and Wilczynski projective normals is given. Canonical bundles of 1st and 2nd kind normals are constructed for each L, L, Hsubbundles of the Hdistribution.
1. Алшибая Э. Д. К геометрии распределений гиперплоскостных элементов в аффинном ...

Fundamentalgroup 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 threeparameter bunch of bundles of fundamentalgroup 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
517

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 n1() 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
1824

Linear and centerprojective quotient groups of the second order differential group
... дифференциальной группы и структурные уравнения расслоения pкореперов // Труды геометрического семинара. М., 1974. Т. 5. С. 239—257.
Kuleshov A.
jet, differential group, frame, bundle, centerprojective group.
8994

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 holonomic, semiholonomic 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 torsionfree and affine space.
1. Лаптев Г. Ф. Основные инфинитезимальные структуры ...

Practical physics lessons based on PC interfaced ADCDAC module
... of analogtodigital and digital toanalog converter (ADCDAC) at practical physics lessons in a college. The authors analyze prepared laboratory class materials in Physics, based on reasonably priced Russianmanufactured «ZET210» DACADC 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 secondorder curvature object contains the curvature object of the fundamentalgroup connection defined in the principal bundle; the curvature object of an affine connection over a manifold; secondorder components. Differential comparisons for the components of the object of curvature of the second order fundamentalgroup 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 centerlinear coframes. The giving fundamental group connection in this fibering is made by means of the centerlinear connection object, not coinciding with the previous objects of connections.
1. Лаптев Г. Ф. Основные ...

Normal connections of the Lsubbundle 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 Lsubbundle of this VH distribution are examined.
1. Попов Ю. И. Сильно взаимные трехсоставные распределения проективного пространства ...