| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2009-08-27T10:16:25Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133391 |
| . |
| 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 |
| . |
