Equipping distributions for linear distribution

Marina F. Grebenyuk; Josef Mikeš

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2007)

  • Volume: 46, Issue: 1, page 35-42
  • ISSN: 0231-9721

Abstract

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In this paper there are discussed the three-component distributions of affine space A n + 1 . Functions { ℳ σ } , which are introduced in the neighborhood of the second order, determine the normal of the first kind of ℋ -distribution in every center of ℋ -distribution. There are discussed too normals { 𝒵 σ } and quasi-tensor of the second order { 𝒮 σ } . In the same way bunches of the projective normals of the first kind of the ℳ -distributions were determined in the differential neighborhood of the second and third order.

How to cite

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Grebenyuk, Marina F., and Mikeš, Josef. "Equipping distributions for linear distribution." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 46.1 (2007): 35-42. <http://eudml.org/doc/32459>.

@article{Grebenyuk2007,
abstract = {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.},
author = {Grebenyuk, Marina F., Mikeš, Josef},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {equipping distributions; linear distribution; affine space; equipping distributions; linear distributions; affine space; tensor of inholonomicity; three component distribution; -distribution},
language = {eng},
number = {1},
pages = {35-42},
publisher = {Palacký University Olomouc},
title = {Equipping distributions for linear distribution},
url = {http://eudml.org/doc/32459},
volume = {46},
year = {2007},
}

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
PB - Palacký University Olomouc
VL - 46
IS - 1
SP - 35
EP - 42
AB - 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.
LA - eng
KW - equipping distributions; linear distribution; affine space; equipping distributions; linear distributions; affine space; tensor of inholonomicity; three component distribution; -distribution
UR - http://eudml.org/doc/32459
ER -

References

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  1. Amisheva N. V., Some questions of affine geometry of the tangential degenerated surface, Kemerov Univ., VINITI, 3826-80, 1980, 17 pp. (in Russian). (1980) 
  2. Grebenjuk M. F., For geometry of H ( M ( Λ ) ) -distribution of affine space, Kaliningrad Univ., Kaliningrad, VINITI, 8204-1388, 1988, 17 pp. (1988) 
  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. (1987) 
  4. Dombrovskyj P. F., To geometry of tangent equipped surfaces in P n , Works of Geometrical Seminar, VINITI, 1975, v. 6, 171–188. (1975) 
  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. (1953) MR0057601
  6. Popov U. I., Inner equipment of degenerated m -dimensional hyperstripe H m r of range r of many-dimensional projective space, Diff. Geometry of Manifolds of Figures, Issue 6, Kaliningrad, 1975, 102–142. (1975) 
  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. (1978) 
  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. (1975) 
  9. Stoljarov A. B., About fundamental objects of regular hyperstripe, News of Univ. Math., 1975, a 10, 97–99. (1975) MR0420478

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