Non-holonomic ( r , s , q ) -jets

Jiří M. Tomáš

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 4, page 1131-1145
  • ISSN: 0011-4642

Abstract

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We generalize the concept of an ( r , s , q ) -jet to the concept of a non-holonomic ( r , s , q ) -jet. We define the composition of such objects and introduce a bundle functor J ˜ r , s , q ℱ ℳ k , l × ℱ ℳ defined on the product category of ( k , l ) -dimensional fibered manifolds with local fibered isomorphisms and the category of fibered manifolds with fibered maps. We give the description of such functors from the point of view of the theory of Weil functors. Further, we introduce a bundle functor J ˜ 1 r , s , q 2 - ℱ ℳ k , l → ℱ ℳ defined on the category of 2 -fibered manifolds with ℱ ℳ k , l -underlying objects.

How to cite

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Tomáš, Jiří M.. "Non-holonomic $(r,s,q)$-jets." Czechoslovak Mathematical Journal 56.4 (2006): 1131-1145. <http://eudml.org/doc/31095>.

@article{Tomáš2006,
abstract = {We generalize the concept of an $(r,s,q)$-jet to the concept of a non-holonomic $(r,s,q)$-jet. We define the composition of such objects and introduce a bundle functor $\{\tilde\{J\}\}^\{r,s,q\}\: \mathcal \{F\}\mathcal \{M\}_\{k,l\} \times \mathcal \{F\}\mathcal \{M\}$ defined on the product category of $(k,l)$-dimensional fibered manifolds with local fibered isomorphisms and the category of fibered manifolds with fibered maps. We give the description of such functors from the point of view of the theory of Weil functors. Further, we introduce a bundle functor $\tilde\{J\}^\{r,s,q\}_1\: 2\text\{-\}\mathcal \{F\}\mathcal \{M\}_\{k,l\} \rightarrow \mathcal \{F\}\mathcal \{M\}$ defined on the category of $2$-fibered manifolds with $\mathcal \{F\}\mathcal \{M\}_\{k,l\}$-underlying objects.},
author = {Tomáš, Jiří M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {bundle functor; jet; non-holonomic jet; Weil bundle; bundle functor; jet; non-holonomic jet; Weil bundle},
language = {eng},
number = {4},
pages = {1131-1145},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-holonomic $(r,s,q)$-jets},
url = {http://eudml.org/doc/31095},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Tomáš, Jiří M.
TI - Non-holonomic $(r,s,q)$-jets
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1131
EP - 1145
AB - We generalize the concept of an $(r,s,q)$-jet to the concept of a non-holonomic $(r,s,q)$-jet. We define the composition of such objects and introduce a bundle functor ${\tilde{J}}^{r,s,q}\: \mathcal {F}\mathcal {M}_{k,l} \times \mathcal {F}\mathcal {M}$ defined on the product category of $(k,l)$-dimensional fibered manifolds with local fibered isomorphisms and the category of fibered manifolds with fibered maps. We give the description of such functors from the point of view of the theory of Weil functors. Further, we introduce a bundle functor $\tilde{J}^{r,s,q}_1\: 2\text{-}\mathcal {F}\mathcal {M}_{k,l} \rightarrow \mathcal {F}\mathcal {M}$ defined on the category of $2$-fibered manifolds with $\mathcal {F}\mathcal {M}_{k,l}$-underlying objects.
LA - eng
KW - bundle functor; jet; non-holonomic jet; Weil bundle; bundle functor; jet; non-holonomic jet; Weil bundle
UR - http://eudml.org/doc/31095
ER -

References

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