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

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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 
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     title = {Equipping distributions for linear distribution},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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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/