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 ...
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 ...
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 ...
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 ...
Strongly mutual threefold distributions of projective space
... distributions is considered as a immersed manifold. By virtue of the -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements , (n-1)-dimensional linear elements  and hyperband distribution . However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately.
Попов Ю. И. Основы теории трехсоставных распределений проективного ...
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 ...
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...
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 ...
Strongly associated threefold distributions of projective space
... distributions is considered as a immersed manifold. By virtue of the SH -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements (n 1)-dimensional linear elements and hyperband distribution. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately. Research was carried out by G. F. Laptev method. Determinations of the H -distributionand existence theorems are ...