Title: | Equipping distributions for linear distribution (English) |

Author: | Grebenyuk, Marina F. |

Author: | Mikeš, Josef |

Language: | English |

Journal: | Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |

ISSN: | 0231-9721 |

Volume: | 46 |

Issue: | 1 |

Year: | 2007 |

Pages: | 35-42 |

Summary lang: | English |

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Category: | math |

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Summary: | In this paper there are discussed the three-component distributions of affine space $A_{n+1}$. Functions $\lbrace \mathcal{M}^\sigma \rbrace $, which are introduced in the neighborhood of the second order, determine the normal of the first kind of $\mathcal{H}$-distribution in every center of $\mathcal{H}$-distribution. There are discussed too normals $\lbrace \mathcal{Z}^\sigma \rbrace $ and quasi-tensor of the second order $\lbrace \mathcal{S}^\sigma \rbrace $. In the same way bunches of the projective normals of the first kind of the $\mathcal{M}$-distributions were determined in the differential neighborhood of the second and third order. (English) |

Keyword: | equipping distributions |

Keyword: | linear distribution |

Keyword: | affine space |

MSC: | 53A15 |

MSC: | 53A45 |

MSC: | 53B05 |

idZBL: | Zbl 1165.53010 |

idMR: | MR2387491 |

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Date available: | 2009-08-27T10:16:25Z |

Last updated: | 2012-05-04 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/133391 |

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Reference: | [1] Amisheva N. V.: Some questions of affine geometry of the tangential degenerated surface.Kemerov Univ., VINITI, 3826-80, 1980, 17 pp. (in Russian). |

Reference: | [2] Grebenjuk M. F.: For geometry of $H(M(\Lambda ))$-distribution of affine space.Kaliningrad Univ., Kaliningrad, VINITI, 8204-1388, 1988, 17 pp. |

Reference: | [3] Grebenjuk M. F.: Fields of geometrical objects of three-component distribution of affine space $A_{n+1}$.Diff. Geometry of Manifolds of Figures: Inter-Univ. subject collection of scientific works, Kaliningrad Univ., 1987, Issue 18, 21–24. |

Reference: | [4] Dombrovskyj P. F.: To geometry of tangent equipped surfaces in $P_n$.Works of Geometrical Seminar, VINITI, 1975, v. 6, 171–188. |

Reference: | [5] Laptev G. F.: Differential geometry of immersed manifolds: Theoretical and group method of differential-geometrical researches.Works of Moscow Mathematical Society, 1953, Vol. 2, 275–382. MR 0057601 |

Reference: | [6] Popov U. I.: Inner equipment of degenerated $m$-dimensional hyperstripe $H^r_m$ of range $r$ of many-dimensional projective space.Diff. Geometry of Manifolds of Figures, Issue 6, Kaliningrad, 1975, 102–142. |

Reference: | [7] Pohila M. M.: Geometrical images, which are associated with many-dimensional stripe of projective space.Abstr. of Rep. of 5th Baltic Geom. Conf., Druskininkaj, 1978, p. 70. |

Reference: | [8] Pohila M. M.: Generalized many-dimensional stripes.Abstr. of Rep. of 6th Conf. of Sov. Union on Modern Problems of Geometry. Vilnius, 1975, 198–199. |

Reference: | [9] Stoljarov A. B.: About fundamental objects of regular hyperstripe.News of Univ. Math., 1975, a 10, 97–99. MR 0420478 |

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