Natural affinors on ( J r , s , q ( . , ℝ 1 , 1 ) 0 ) *

Włodzimierz M. Mikulski

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 4, page 655-663
  • ISSN: 0010-2628

Abstract

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Let r , s , q , m , n ∈ ℕ be such that s ≥ r ≤ q . Let Y be a fibered manifold with m -dimensional basis and n -dimensional fibers. All natural affinors on ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * are classified. It is deduced that there is no natural generalized connection on ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * . Similar problems with ( J r , s ( Y , ℝ ) 0 ) * instead of ( J r , s , q ( Y , ℝ 1 , 1 ) 0 ) * are solved.

How to cite

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Mikulski, Włodzimierz M.. "Natural affinors on $(J^{r,s,q}(.,\mathbb {R}^{1,1})_0)^*$." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 655-663. <http://eudml.org/doc/248782>.

@article{Mikulski2001,
abstract = {Let $r,s,q, m,n\in \mathbb \{N\}$ be such that $s\ge r\le q$. Let $Y$ be a fibered manifold with $m$-dimensional basis and $n$-dimensional fibers. All natural affinors on $(J^\{r,s,q\}(Y,\mathbb \{R\}^\{1,1\})_0)^*$ are classified. It is deduced that there is no natural generalized connection on $(J^\{r,s,q\}(Y,\mathbb \{R\}^\{1,1\})_0)^*$. Similar problems with $(J^\{r,s\}(Y,\mathbb \{R\})_0)^*$ instead of $(J^\{r,s,q\}(Y,\mathbb \{R\}^\{1,1\})_0)^*$ are solved.},
author = {Mikulski, Włodzimierz M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {bundle functors; natural transformations; natural affinors; bundle functors; natural transformations; natural affinors},
language = {eng},
number = {4},
pages = {655-663},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Natural affinors on $(J^\{r,s,q\}(.,\mathbb \{R\}^\{1,1\})_0)^*$},
url = {http://eudml.org/doc/248782},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Natural affinors on $(J^{r,s,q}(.,\mathbb {R}^{1,1})_0)^*$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 4
SP - 655
EP - 663
AB - Let $r,s,q, m,n\in \mathbb {N}$ be such that $s\ge r\le q$. Let $Y$ be a fibered manifold with $m$-dimensional basis and $n$-dimensional fibers. All natural affinors on $(J^{r,s,q}(Y,\mathbb {R}^{1,1})_0)^*$ are classified. It is deduced that there is no natural generalized connection on $(J^{r,s,q}(Y,\mathbb {R}^{1,1})_0)^*$. Similar problems with $(J^{r,s}(Y,\mathbb {R})_0)^*$ instead of $(J^{r,s,q}(Y,\mathbb {R}^{1,1})_0)^*$ are solved.
LA - eng
KW - bundle functors; natural transformations; natural affinors; bundle functors; natural transformations; natural affinors
UR - http://eudml.org/doc/248782
ER -

References

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  8. Mikulski W.M., Natural affinors on r -jet prolongation of the tangent bundles, Arch. Math. Brno 34(2) (1998), 321-328. (1998) MR1645340
  9. Mikulski W.M., Natural affinors on ( J r T * ) * , Arch. Math. Brno 36(4) (2000), 261-267. (2000) MR1811170
  10. Mikulski W.M., The natural affinors on ø t i m e s k T ( r ) , Note di Matematica 19(2) (1999), 269-274. (1999) MR1816880
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