Non-existence of some canonical constructions on connections
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 4, pp. 691-695
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For a vector bundle functor $H:\Cal M f\to \Cal V\Cal B$ with the point property we prove that $H$ is product preserving if and only if for any $m$ and $n$ there is an $\Cal F\Cal M_{m,n}$-natural operator $D$ transforming connections $\Gamma$ on $(m,n)$-dimensional fibered manifolds $p:Y\to M$ into connections $D(\Gamma)$ on $Hp:HY\to HM$. For a bundle functor $E:\Cal F\Cal M_{m,n}\to \Cal F\Cal M$ with some weak conditions we prove non-existence of $\Cal F\Cal M_{m,n}$-natural operators $D$ transforming connections $\Gamma$ on $(m,n)$-dimensional fibered manifolds $Y\to M$ into connections $D(\Gamma)$ on $EY\to M$.
@article{CMUC_2003__44_4_a12,
author = {Mikulski, W. M.},
title = {Non-existence of some canonical constructions on connections},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {691--695},
publisher = {mathdoc},
volume = {44},
number = {4},
year = {2003},
mrnumber = {2062885},
zbl = {1099.58004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2003__44_4_a12/}
}
TY - JOUR AU - Mikulski, W. M. TI - Non-existence of some canonical constructions on connections JO - Commentationes Mathematicae Universitatis Carolinae PY - 2003 SP - 691 EP - 695 VL - 44 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMUC_2003__44_4_a12/ LA - en ID - CMUC_2003__44_4_a12 ER -
Mikulski, W. M. Non-existence of some canonical constructions on connections. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 4, pp. 691-695. http://geodesic.mathdoc.fr/item/CMUC_2003__44_4_a12/