Fields of geometric objects associated with compiled hyperplaneH H(Λ,L) -distribution in affine space

Autor: Yu. I. Popov
Jazyk: English<br />Russian
Rok vydání: 2020
Předmět:
Zdroj: Дифференциальная геометрия многообразий фигур, Iss 51, Pp 103-115 (2020)
Druh dokumentu: article
ISSN: 0321-4796
2782-3229
DOI: 10.5922/0321-4796-2020-51-12
Popis: 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.
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