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Differential Geometry of Manifolds

2026 №57 (1)

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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.


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