Contact elements on fibered manifolds

Ivan Kolář; Włodzimierz M. Mikulski

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 4, page 1017-1030
  • ISSN: 0011-4642

Abstract

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For every product preserving bundle functor T μ on fibered manifolds, we describe the underlying functor of any order ( r , s , q ) , s ≥ r ≤ q . We define the bundle K k , l r , s , q Y of ( k , l ) -dimensional contact elements of the order ( r , s , q ) on a fibered manifold Y and we characterize its elements geometrically. Then we study the bundle of general contact elements of type μ . We also determine all natural transformations of K k , l r , s , q Y into itself and of T ( K k , l r , s , q Y ) into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from Y to K k , l r , s , q Y .

How to cite

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Kolář, Ivan, and Mikulski, Włodzimierz M.. "Contact elements on fibered manifolds." Czechoslovak Mathematical Journal 53.4 (2003): 1017-1030. <http://eudml.org/doc/30832>.

@article{Kolář2003,
abstract = {For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_\{k,l\}^\{r,s,q\} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_\{k,l\}^\{r,s,q\} Y$ into itself and of $T(K_\{k,l\}^\{r,s,q\} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_\{k,l\}^\{r,s,q\} Y$.},
author = {Kolář, Ivan, Mikulski, Włodzimierz M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {jet of fibered manifold morphism; contact element; Weil bundle; natural operator; jet of fibered manifold morphism; contact element; Weil bundle; natural operator},
language = {eng},
number = {4},
pages = {1017-1030},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Contact elements on fibered manifolds},
url = {http://eudml.org/doc/30832},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Kolář, Ivan
AU - Mikulski, Włodzimierz M.
TI - Contact elements on fibered manifolds
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 1017
EP - 1030
AB - For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$.
LA - eng
KW - jet of fibered manifold morphism; contact element; Weil bundle; natural operator; jet of fibered manifold morphism; contact element; Weil bundle; natural operator
UR - http://eudml.org/doc/30832
ER -

References

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  1. Jet manifold associated to a Weil bundle, Arch. Math. (Brno) 36 (2000), 195–199. (2000) Zbl1049.58007MR1785036
  2. Prolongation of projectable tangent valued forms, To appear in Rendiconti Palermo. MR1942654
  3. On the jets of fibered manifold morphisms, Cahiers Topo. Géom. Diff. Catégoriques XL (1999), 21–30. (1999) MR1682575
  4. Oeuvres complètes et commentées. Parties I-A et I-2, Cahiers Topo. Géom. Diff. XXIV (1983). (1983) 
  5. 10.1017/S0027763000007339, Nagoya Math. J. 158 (2000), 99–106. (2000) MR1766571DOI10.1017/S0027763000007339
  6. Covariant approach to natural transformations of Weil functors, Comment. Math. Univ. Carolin. 27 (1986), 723–729. (1986) MR0874666
  7. Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) MR1202431
  8. Natural lifting of connections to vertical bundles, Supplemento ai Rendiconti del Circolo Mat. di Palermo, Serie II 63 (2000), 97–102. (2000) MR1758084
  9. 10.1007/BF01292769, Mh. Math. 119 (1995), 63–77. (1995) Zbl0823.58004MR1315684DOI10.1007/BF01292769
  10. Product preserving bundle functors on fibered manifolds, Arch. Math. (Brno) 32 (1996), 307–316. (1996) Zbl0881.58002MR1441401
  11. 10.1023/A:1022408527395, Czechoslovak Math. J. 50 (2000), 721–748. (2000) MR1792967DOI10.1023/A:1022408527395
  12. Natural operators transforming projectable vector fields to products preserving bundles, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II 59 (1999), 181–187. (1999) MR1692269
  13. Théorie des points proches sur les variétés différentielles, Collogue de C.N.R.S, Strasbourg, 1953, pp. 111–117. (1953) MR0061455

Citations in EuDML Documents

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  1. Miroslav Kureš, Włodzimierz M. Mikulski, Natural operators lifting vector fields to bundles of Weil contact elements
  2. Jan Kurek, Włodzimierz Mikulski, The natural functions on the cotangent bundle of higher order vector tangent bundles over fibered manifolds
  3. Miroslav Doupovec, Ivan Kolář, Włodzimierz M. Mikulski, On the jets of foliation respecting maps
  4. Jan Kurek, Włodzimierz M. Mikulski, The natural affinors on some fiber product preserving gauge bundle functors of vector bundles
  5. Włodzimierz M. Mikulski, Natural affinors on ( J r , s , q ( . , ℝ 1 , 1 ) 0 ) *

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