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 ...
Normalizations of hyperband
Mission and proof of existence theorem for hyperband m n SH A which carrier conjugated system (; * ) of planar elements are examined: the tangent subbundle of (; * ) -planes (-subbundle) and the tangent subbundle of lines (* -subbundle). Internal beams of normalizations of hyperband m SH and its tangent subbundles in the second-order differential neighborhood are constructed.
1. Вагнер ...
Normal connections of the L-subbundle of a strongly mutual distribution of the projective space
... the incidence relation of the elements of the -, M-, H-subbundle has an appearance X r 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 ...
Bundles of Projective Normals of the Hyperband Distribution of an Affine Space
... 1954. Т. 97. С. 716—776.
8. Лаптев Г. Ф. Гиперповерхности в пространстве проективной связности // Докл. АН СССР. 1958. Т. 121, № 1. С. 41—44.
Popov Y. I.
distribution, subbundle, bundle, quasitensor, internal normalization, projectivity Bompiani — Pantazi, geometrical object
69-75
The curvature object of the fundamental-group connection of the second-order
... теории трехсоставных распределений проективного пространства. СПб., 1992.
7. Mihailescu T. Geometrie differentiala projectiva. Bucaresti Acad. RPR, 1958.
Ryazanov N.
normalization, quasitensor, subbundle, Bompiani–Pantazi bijection, geometrical object coverage, hypersurface
10-15
Creation of the Norden normalization of the L-, E-subbundles of the SH -distribution of the projective space
Norden 1st and 2nd kind inner normals of the L-, E-subbundle of a special class (SH -distribution) of the regular threefold distributions (H -distributions) of the projective space are constructed.
1. Попов Ю. И. Сильно взаимные трехсоставные распределения проективного пространства // Вестник Балтийского федерального университета им. И. Канта. 2015. Вып. 10. С. 62—76....
Eliseeva N. A., Popov Y. I.
The authors construct Foss and Green's normalizations in Norden's sense internally invariantly. The research sets tangent affine connections and tangent central affine connections of the main structural subbundles of H(L, L)-distribution of affine space.
1. Попов Ю. И. Нормализация основных структурных подрасслоений H(L, L)-распределения аффинного пространства ...
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 of H(, L)-distribution are constructed.
1. Попов Ю. И. Скомпонованные ...
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 of the main structural subbundles of the SH-distribution are introduced.
1. Попов Ю. И. О проективно-дифференциальной ...
Introduction of connections on a hypersurface ()
The paper introduces internal affine (tangent) and normal (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,...
The differential and geometrical structures associated with the regular tangently r-framed hyperstrip of the projective space
... Дифференциально-геометрические структуры на дифференцируемых многообразиях // Там же. 1977. Т. 8. С. 89—111.
Popov Ju.
hyperstrip, -structure, T-structure, almost contact structure, tangent framing, subbundle, projective space
52-63
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 Ю. И. Поля геометрических объектов гиперполосного распределения аффинного пространства ...
Representation of projective connections on the SH -distribution of the projective space
Projective connections defined by projection and associated to subbundles , L, E of the strong dual threefold distribution (the SH -distribution) of the projective space are constructed. Coverages of torsion-curvature tensors components of the constructed projective connections , , of subbundles ,...
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 ...
Fields of fundamental and captured geometrical objects of the 2nd or-der H-distribution of affine space
... аффинного пространства / Калининградский гос. ун-т. Деп. в ВИНИТИ, № 6807-В87Деп., 1986.
6. Норден А. П. Пространства аффинной связности. М., 1976.
Popov Ju.
subbundle, normalization, normal, tensor, quasitensor, distribution, coincidence, Bompiani–Pantazi bijection, envelopment of geometrical object
18-24
Invariant normalizations and É. Cartan equips of main structural subbundles of SH-distribution
SH-distribution and the theorem of the existence in frame of order zero are given. Invariant normalizations, matchings Bompiani-Pantazi and equipments in order of E. Cartan of major structural sub-bundles are built.
1. Будылкин А. А. Инвариантные нормализации скомпонованного гиперплоскостного распределения проективного пространства // Естественные и математические...
Strongly associated threefold distributions of projective space
.... деп. ВИНИТИ 16.12.1982. № 6192-82Деп.
11. Норден А. П. Пространства аффинной связности. М., 1976.
Popov Ju.
distribution, duality of distribution, adjoint surface system, tensor, quasitensor, subbundle, quasinormal
5-18
Strongly mutual threefold distributions of projective space
... многообразий. // Тр. моск. мат. об-ва. 1953. Т.2. С. 275 382.
Popov Yu.
distribution, nonholonomic tensor, holonomic distribution, hyperband, tensor, quasitensor, duality of distribution, adjoint surface system, quasinormal, subbundle.
62-67
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 L-subbundle is introduced.
1. Остиану Н. М. Распределение гиперплоскостных элементов в проективном пространстве // Труды геометрического...