Search
Submit an article RU
Differential Geometry of Manifolds

Current issue

Back to the list Download the article
ENG
Сохранить XML для: JATS (вып.)
RUS
Сохранить XML для: JATS (вып.)
Shevchenko Yu.I. Vyalova A.V.

Induced connections of two types on a distribution of the second kind

DOI
10.5922/0321-4796-2026-57-1-8
Pages
93-101
projective space distribution of the second kind connec­tion equipment

Abstract

In a projective space a distribution of the second kind inde­pendently of the geometry of distributions of the first kind is stu­died. A distribution of the second kind is understood as an n-di­mensional manifold of multidimensional planes obtained by as­signing to each point of the space a plane not passing through that point. In the principal bundle associated with the distribution, a connection is given. An equipment of the distribution of the sec­ond kind is constructed; it is a field of planes that, together with the generating point and the generating plane, forms a three-term composition in the sense of Norden. It is proved that the distribu­tion and its equipment induce connections of two types in the as­sociated bundle. Conditions for the coincidence of these connec­tions are found.


Reference

1. Shevchenko, Yu. I.: Clothing of centreprojective manifolds. Kali­ningrad (2000).

2. Ostianu, N. M. Distribution of hyperplane elements in projective space. Tr. Geom. sem., 4, 71—120 (1973).

3. Omelyan, O. M. About а coincidence of group connections induced by an internal composition equipment of a distribution. Math. Notes, 102:6, 896—907 (2017).

4. Omelyan, O. M. Geometrization of a sheaf of first-type connections generated by a compositional frame on a distribution of planes. Itogi Nauki i Tekhn. Sovrem. Math. and its App. Theme Reviews, 180, 69—73 (2020).

5. Shevchenko, Yu. I.: Degeneration of plane affine Stolyarov connec­tions. Fund. i Prikl. Mat., 16:2, 155—161 (2010).

6. Polyakova, K., Shevchenko, Yu.: Laptev — Lumiste’s methods of giving connection and geometrical vectors. DGMF, 49, 19—28 (2018).

7. Shevchenko, Yu.: Laptev’s and Lumiste’s ways of connection rep­resentation in the principal fibre bundle. DGMF, 37, 185—193 (2006).

8. Evtushik, L. E., Lumiste, Yu. G., Ostianu, N. M., Shirokov, A. P.: Dif­ferential-geometric structures on manifolds. Itogi Nauki i Tekhn. Probl. Geom., 9, Moscow (1979).

9. Belova, O. O.: Connections in fiberings associated with the Grass­man manifold and the space of centered planes. J. Math. Sci., 162:5, 605—632 (2009).

10. Belova, O. O.: The deformation pseudotensor of connections in co­con­gruence . DGMF, 54(1), 39—48 (2023).