Geodesic
Equipping distributions for linear distribution
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 46 (2007) no. 1, pp. 35-42 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 53A15, 53A45, 53B05
Keywords: equipping distributions; linear distribution; affine space 
@article{AUPO_2007_46_1_a3,
     author = {Grebenyuk, Marina F. and Mike\v{s}, Josef},
     title = {Equipping distributions for linear distribution},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {35--42},
     year = {2007},
     volume = {46},
     number = {1},
     mrnumber = {2387491},
     zbl = {1165.53010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2007_46_1_a3/}
}
TY  - JOUR
AU  - Grebenyuk, Marina F.
AU  - Mikeš, Josef
TI  - Equipping distributions for linear distribution
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2007
SP  - 35
EP  - 42
VL  - 46
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUPO_2007_46_1_a3/
LA  - en
ID  - AUPO_2007_46_1_a3
ER  - 
%0 Journal Article
%A Grebenyuk, Marina F.
%A Mikeš, Josef
%T Equipping distributions for linear distribution
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2007
%P 35-42
%V 46
%N 1
%U http://geodesic.mathdoc.fr/item/AUPO_2007_46_1_a3/
%G en
%F AUPO_2007_46_1_a3
Grebenyuk, Marina F.; Mikeš, Josef. Equipping distributions for linear distribution. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 46 (2007) no. 1, pp. 35-42. http://geodesic.mathdoc.fr/item/AUPO_2007_46_1_a3/

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

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

[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.

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

[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

[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.

[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.

[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.

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