Strongly mutual threefold distributions of projective space :: IKBFU's united scientific journal editorial office

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Strongly mutual threefold distributions of projective space

Author Popov Yu.
Pages 62-67
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Keywords distribution, nonholonomic tensor, holonomic distribution, hyperband, tensor, quasitensor, duality of distribution, adjoint surface system, quasinormal, subbundle.
Abstract (summary) Construction of a general theory of a special class ( -distribution) of the regular threefold distributions ( -distribution [1]) of the projective space   consisting of a basic distribution of the 1st kind of r-dimensional planes   are equipped with the distribution of the 1st kind of m-dimensional planes   and equip distribution 1st the first kind of hyperplane elements (hyperplanes)   with the ratio of the incidence of the corresponding elements in the common center   is considered in this article. In this paper, these three 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 [2], (n-1)-dimensional linear elements [3]  and hyperband distribution [4]. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately.
References Попов Ю. И. Основы теории трехсоставных распределений проективного пространства : монография. СПб., 1992.
2. Лаптев Г. Ф., Остиану Н. М. Распределения m-мерных линейных элементов в пространстве проективной связности// Тр. геом. семинара. ВИНИТИ АН СССР. М., 1971. Т.3. С. 49 94.
3. Остиану Н. М. Распределение гиперплоскостных элементов в проективном пространстве. // Там же. 1973. Т.4. С. 71 120.
4. Столяров А. В. Проективно-дифференциальная геометрия регулярного гиперполосного распределения m-мерных линейных элементов// Проблемы геометрии. Итоги науки и техники. ВИНИТИ АН СССР. М., 1975. Т.7. С. 117 151.
5. Лаптев Г. Ф. Дифференциальная геометрия погруженных многообразий. // Тр. моск. мат. об-ва. 1953. Т.2. С. 275 382.

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