Нормализации Нордена — Чакмазяна распределений, заданных на гиперповерхности
- DOI
- 10.5922/0321-4796-2020-51-8
- Страницы / Pages
- 68-75
Аннотация
В проективном пространстве продолжаем изучать гиперповерхность, несущую тройку сильно взаимных распределений. Для оснащающих распределений гиперповерхности внутренним образом введена нормализация в смысле Нордена — Чакмазяна.
Abstract
In the projective space, we continue to study a hypersurface with three strongly mutual distributions. For equipping distributions of a hypersurface, normalization in the sense of Norden — Chakmazyan is introduced internally. The distribution of the equipping planes is normalized in the sense of Norden — Chakmazyan if the fields of normals of the 1st kind and normals of the 2nd kind are attached to it in an invariant way. For each equipping distribution, the fields of normals of the 1st and 2nd kind are defined by the corresponding fields of quasitensors. At each point of the hypersurface, the normal of the 1st kind of the equipping distribution of the hypersurface passes through the characteristic of the tangent hypersurface. This characteristic was obtained with displacements of the point along the integral curves of the equipping distribution. For equipping distributions, the coverage of quasitensors is found under which the conditions of invariance of the normals of the 1st and 2nd kind are satisfied. Coverage of quasitensors is found for which normalization in the sense of Norden — Chakmazyan is attached to the equipping distributions of the hypersurface in a second-order differential neighborhood.
Список литературы
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Reference
1. Eliseeva, N. А.: Hypersurfaces of projective space equipped with distributions. DGMF. Kaliningrad. 44, 52—63 (2013).
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