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• Giving the 1st order affine connection by means of the 2nd order vector-valued forms

  ... 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 in bundle of tangent lin-ear 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 non-holonomicity 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 Grassman-like 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, Grassman-like manifold, normal generalized affine connection, torsion tensor, curvature tensor. 156-159

• 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 5-17

• A Grouped Hyperplane Distribution of an Affine Space

  In this article, I determine the grouped hyperplane distribution of the affine space An (SH-distribution) and prove the relevant existence theorem. I perform internal normalizations of the main structural subbundles of the SH-distribution in first and second-order 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 Akivis-Laptev 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 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 высших поряд-ков 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. 166-172

• 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 three-parametrical family of ellipsoids

  A three-parametrical family of ellipsoids in three-dimensional 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 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 // ...

• About fields of geometrical objects connected with the complex central nondegenerate hyperquadrics

  A field of some geometrical objects internally connected with a complex (n-parametrical family) of the central nondegenerate hyperquadrics in n-dimensional 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 (H-distribution) is given and its existence theorem is proved. Conditions of holonomic H-distribution is determined and Bompiani—Pantazi bijection between the first kind normal and the second one for associated with H-distribution 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 (L-virual 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-, H-subbundle correspond to them ...

• 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 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-, 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 пространстве // Тр. геом. семинара...

• Three-parametrical collection of ellipsoids assumed a construction

  A subclass of three-parametrical collection of ellipsoids in three-dimensional 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 three-dimensional modeling of dragline waste rehandling

  ... developed a prototype of that information and analytical technology for modeling dragline waste rehandling in three-dimensional space through two-dimensional 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. 127-134