Non-existence of some canonical constructions on connections

Mikulski, Włodzimierz M.. "Non-existence of some canonical constructions on connections." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 691-695. <http://eudml.org/doc/249186>.

@article{Mikulski2003,
abstract = {For a vector bundle functor $H:\mathcal \{M\} f\rightarrow \mathcal \{V\}\mathcal \{B\}$ with the point property we prove that $H$ is product preserving if and only if for any $m$ and $n$ there is an $\mathcal \{F\}\mathcal \{M\}_\{m,n\}$-natural operator $D$ transforming connections $\Gamma $ on $(m,n)$-dimensional fibered manifolds $p:Y\rightarrow M$ into connections $D(\Gamma )$ on $Hp:HY\rightarrow HM$. For a bundle functor $E:\mathcal \{F\}\mathcal \{M\}_\{m,n\}\rightarrow \mathcal \{F\}\mathcal \{M\}$ with some weak conditions we prove non-existence of $\mathcal \{F\}\mathcal \{M\}_\{m,n\}$-natural operators $D$ transforming connections $\Gamma $ on $(m,n)$-dimensional fibered manifolds $Y\rightarrow M$ into connections $D(\Gamma )$ on $EY\rightarrow M$.},
author = {Mikulski, Włodzimierz M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {(general) connection; natural operator; natural operator},
language = {eng},
number = {4},
pages = {691-695},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-existence of some canonical constructions on connections},
url = {http://eudml.org/doc/249186},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Non-existence of some canonical constructions on connections
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 4
SP - 691
EP - 695
AB - For a vector bundle functor $H:\mathcal {M} f\rightarrow \mathcal {V}\mathcal {B}$ with the point property we prove that $H$ is product preserving if and only if for any $m$ and $n$ there is an $\mathcal {F}\mathcal {M}_{m,n}$-natural operator $D$ transforming connections $\Gamma $ on $(m,n)$-dimensional fibered manifolds $p:Y\rightarrow M$ into connections $D(\Gamma )$ on $Hp:HY\rightarrow HM$. For a bundle functor $E:\mathcal {F}\mathcal {M}_{m,n}\rightarrow \mathcal {F}\mathcal {M}$ with some weak conditions we prove non-existence of $\mathcal {F}\mathcal {M}_{m,n}$-natural operators $D$ transforming connections $\Gamma $ on $(m,n)$-dimensional fibered manifolds $Y\rightarrow M$ into connections $D(\Gamma )$ on $EY\rightarrow M$.
LA - eng
KW - (general) connection; natural operator; natural operator
UR - http://eudml.org/doc/249186
ER -