Current issue

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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