A construction of a connection on $GY\to Y$ from a connection on $Y\to M$ by means of classical linear connections on $M$ and $Y$

Mikulski, Włodzimierz M.. "A construction of a connection on $GY\rightarrow Y$ from a connection on $Y\rightarrow M$ by means of classical linear connections on $M$ and $Y$." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 759-770. <http://eudml.org/doc/249528>.

@article{Mikulski2005,
abstract = {Let $G$ be a bundle functor of order $(r,s,q)$, $s\ge r\le q$, on the category $\mathcal \{F\}\mathcal \{M\}_\{m,n\}$ of $(m,n)$-dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $\Gamma $ on an $\mathcal \{F\}\mathcal \{M\}_\{m,n\}$-object $Y\rightarrow M$ we construct a general connection $\mathcal \{G\}(\Gamma ,\lambda ,\Lambda )$ on $GY\rightarrow Y$ be means of an auxiliary $q$-th order linear connection $\lambda $ on $M$ and an $s$-th order linear connection $\Lambda $ on $Y$. Then we construct a general connection $\mathcal \{G\} (\Gamma ,\nabla _1,\nabla _2)$ on $GY\rightarrow Y$ by means of auxiliary classical linear connections $\nabla _1$ on $M$ and $\nabla _2$ on $Y$. In the case $G=J^1$ we determine all general connections $\mathcal \{D\}(\Gamma ,\nabla )$ on $J^1Y\rightarrow Y$ from general connections $\Gamma $ on $Y\rightarrow M$ by means of torsion free projectable classical linear connections $\nabla $ on $Y$.},
author = {Mikulski, Włodzimierz M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {general connection; classical linear connection; bundle functor; natural operator; general connection; classical linear connection; bundle functor; natural operator},
language = {eng},
number = {4},
pages = {759-770},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A construction of a connection on $GY\rightarrow Y$ from a connection on $Y\rightarrow M$ by means of classical linear connections on $M$ and $Y$},
url = {http://eudml.org/doc/249528},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - A construction of a connection on $GY\rightarrow Y$ from a connection on $Y\rightarrow M$ by means of classical linear connections on $M$ and $Y$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 759
EP - 770
AB - Let $G$ be a bundle functor of order $(r,s,q)$, $s\ge r\le q$, on the category $\mathcal {F}\mathcal {M}_{m,n}$ of $(m,n)$-dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $\Gamma $ on an $\mathcal {F}\mathcal {M}_{m,n}$-object $Y\rightarrow M$ we construct a general connection $\mathcal {G}(\Gamma ,\lambda ,\Lambda )$ on $GY\rightarrow Y$ be means of an auxiliary $q$-th order linear connection $\lambda $ on $M$ and an $s$-th order linear connection $\Lambda $ on $Y$. Then we construct a general connection $\mathcal {G} (\Gamma ,\nabla _1,\nabla _2)$ on $GY\rightarrow Y$ by means of auxiliary classical linear connections $\nabla _1$ on $M$ and $\nabla _2$ on $Y$. In the case $G=J^1$ we determine all general connections $\mathcal {D}(\Gamma ,\nabla )$ on $J^1Y\rightarrow Y$ from general connections $\Gamma $ on $Y\rightarrow M$ by means of torsion free projectable classical linear connections $\nabla $ on $Y$.
LA - eng
KW - general connection; classical linear connection; bundle functor; natural operator; general connection; classical linear connection; bundle functor; natural operator
UR - http://eudml.org/doc/249528
ER -