
Giving the 1st order affine connection by means of the 2nd order vectorvalued forms
... 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 in bundle of tangent linear frames defines linear operator from 1st order cotangent space (space of forms of degree 1) in cotangent space of 2nd order. It is proved that affine connection in bundle of tangent linear frames defines horizontal ...

Semiholonomical, holonomical and trivial spaces of affine connection
... and trivial manifolds are defined. The Ricci’s identities allowed us to prove semiholonomicity of the space An,n. This semiholonomicity preserves in the space without torsion A’n,n and in the space without curvature ‘An,n , besides the locally affine space Ά’n,n is trivial. Tensor of nonholonomicity of the space An,n is introduced. Vanishing of this tensor makes the space holonomic, H n n A . Also curvature tensor of associated space of affine connection without torsion A’n,n was introduced....

Normal generalized affine connection associated with the Grassmanlike manifold of centred planes
... многообр. фигур. Калининград, 2009. Вып.
40. С. 18—28.
4.
Шевченко
Ю. И.
Оснащения центропроективных многообразий. Калининград, 2000.
Belova O. O.
projective space, Grassmanlike manifold, normal generalized affine connection, torsion tensor,
curvature tensor.
156159

Eliseeva N. A., Popov Y. I.
... Швейкин П. И. Очерк 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

A Grouped Hyperplane Distribution of an Affine Space
In this article, I determine the grouped hyperplane distribution of the affine space An (SHdistribution) and prove the relevant existence theorem. I perform internal normalizations of the main structural subbundles of the SHdistribution in first and secondorder differential neighbourhoods. Normal and tangent affine connections ...

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 AkivisLaptev on the surface. It is shown that the surface of an affine space is a holonomic smooth manifold.
1. Акивис ...

Hierarchies of smooth manifolds up to zeroth and first orders
... 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 высших порядков на гладком многообразии // Тр. геом. семин. / ВИНИТИ. М., 1966. Т. 1. С. 139—189....

A semicanonical normal affine connection associated with the distribution
...
Шевченко Ю. И
. Связности, ассоциированные с распределением плоскостей в проективном пространстве. Калининград, 2009.
Shevchenko Yu. I.
projective space, distribution of planes, affine connection, linear connection, connection object,
curvature tensor, torsion tensor, semiholonomity.
166172

About fields of geometrical objects of the H distribution of the affine space
A creation of geometric objects of the hyperband distribution (H distribution) of affine space An in the differential 1–3rd orders neighborhoods is continued. As a result a number of new normalization in Norden's sense of the main structural subbundles of this H distribution are constructed (are found) internally invariantly.
1. Попов ...

Normalization of the basic structural subbundles of the H(, L)distribution of affine space
The author pioneers to study a special class of the grouped hyperplane distributions — the H(, L)distribution of affine space. He introduces Bompiani — Pantazi correspondences associated with the main structural subbundles of the H(, L)distribution of affine space. Norden’s normalizations of the main structural subbundles in the differential 1st and 2nd order neighbourhoods ...

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,...

A geometric model of a threeparametrical family of ellipsoids
A threeparametrical family of ellipsoids in threedimensional affine space with special geometric properties is considered. A geometrical model of this manifold is constructed.
1. Кретов М. В. Комплексы эллипсоидов в аффинном пространстве // Диф.геом. многообр....

Fields of fundamental and captured geometrical objects of the 2nd order Hdistribution of affine space
Norden inner normalization fields of basic structural Λ, L, Hsubbundle of hyperband Hdistribution 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 распределения аффинного пространства // ...

About fields of geometrical objects connected with the complex central nondegenerate hyperquadrics
A field of some geometrical objects internally connected with a complex (nparametrical family) of the central nondegenerate hyperquadrics in ndimensional affine space are defined and their geometrical sense is found out.
1. Кретов М. В. Дифференцируемые многообразия, ассоциированные с комплексами центральных невырожденных ...

Voss and Green's normalizations of hyperband distribution of affine space
Voss and Green's normalizations of the main structural subbundles of hyperband distribution of H distribution of affine space are constructed internally invariantly.
1. Попов Ю. И. Введение в теорию регулярного гиперполостного распределения аффинного пространства // Вестник Балтийского ...

Introduction to a theory of regular hyperband distribution of an affine space
Regular hyperband distribution of an affine space (Hdistribution) is given and its existence theorem is proved. Conditions of holonomic Hdistribution is determined and Bompiani—Pantazi bijection between the first kind normal and the second one for associated with Hdistribution H, Λ and ...

Normalization of basic structural subbundle of distribution in second order differential neighborhood
Norden inner normalization fields of basic structural subbundle of hyperband distribution are constructed in second order differential neighborhood of affine space. It is showed that first order normal (Lvirual affine normal, Blashke normal, Trenson normal) corresponding to each of subbundle belongs to the same sheaf in any center A. Sheafs of second order normal of Λ, L, Hsubbundle correspond to them ...

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 the curvature object forms a geometric ...

Bundles of Projective Normals of the Hyperband Distribution of an Affine Space
It is shown that the H 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 пространстве // Тр. геом. семинара...

Threeparametrical collection of ellipsoids assumed a construction
A subclass of threeparametrical collection of ellipsoids in threedimensional affine space is investigated. The construction of the considered manifold is given.
1. Кретов М. В. Комплексы эллипсоидов в аффинном пространстве // Диф.геом. многообр. фигур. 1979. С. 41—47....

The application of the method of average sections with coordinate transformation in threedimensional modeling of dragline waste rehandling
... developed a prototype of that information and analytical technology for modeling dragline waste rehandling in threedimensional space through twodimensional numerical algorithms. Using the methods of analytical geometry and mathematical statistics, a number ... ... Вып. 10. С. 114—120.
Nazarov I., Bryksin V., Savelenko V.
dragline, grid models of surface, regression equation, affine transformation.
127134