### Fields of geometric objects associated with compiled hyperplane -distribution in affine space

- DOI
- 10.5922/0321-4796-2020-51-12
- Pages
- 103-115

#### Abstract

A compiled hyperplane distribution is considered in an n-dimensional projective space . We will briefly call it a -distribution. Note that the plane L(A) is the distribution characteristic obtained by displacement in the center belonging to the L-subbundle. The following results were obtained:

a) The existence theorem is proved: -distribution exists with arbitrary (3n – 5) functions of n arguments.

b) A focal manifold is constructed in the normal plane of the 1st kind of L-subbundle. It was obtained by shifting the center A along the curves belonging to the L-distribution. A focal manifold is also given, which is an analog of the Koenigs plane for the distribution pair (L, L).

c) It is shown that a framed -distribution in the 1st kind normal field of H-distribution induces tangent and normal bundles.

d) Six connection theorems induced by a framed -distribution in these bundles are proved.

In each of the bundles , the framed -distribution induces an intrinsic torsion-free affine connection in the tangent bundle and a centro-affine connection in the corresponding normal bundle.

e) In each of the bundles (d) in the differential neighborhood of the 2nd order, the covers of 2-forms of curvature and curvature tensors of the corresponding connections are constructed.

#### Reference

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