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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  11. 10.1023/A:1022408527395, Czechoslovak Math. J. 50 (2000), 721–748. (2000) MR1792967DOI10.1023/A:1022408527395
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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. Włodzimierz M. Mikulski, Natural affinors on ( J r , s , q ( . , ℝ 1 , 1 ) 0 ) *
  5. Jan Kurek, Włodzimierz M. Mikulski, The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

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