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. |
| Databáze: | Directory of Open Access Journals |
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