On the Kolář connection

Mikulski, Włodzimierz M.. "On the Kolář connection." Archivum Mathematicum 049.4 (2013): 223-240. <http://eudml.org/doc/260831>.

@article{Mikulski2013,
abstract = {Let $Y\rightarrow M$ be a fibred manifold with $m$-dimensional base and $n$-dimensional fibres and $E\rightarrow M$ be a vector bundle with the same base $M$ and with $n$-dimensional fibres (the same $n$). If $m\ge 2$ and $n\ge 3$, we classify all canonical constructions of a classical linear connection $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ on $Y$ from a system $(\Gamma ,\Lambda ,\Phi ,\Delta )$ consisting of a general connection $\Gamma $ on $Y\rightarrow M$, a torsion free classical linear connection $\Lambda $ on $M$, a vertical parallelism $\Phi \colon Y\times _ME\rightarrow VY$ on $Y$ and a linear connection $\Delta $ on $E\rightarrow M$. An example of such $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ is the connection $(\Gamma ,\Lambda ,\Phi ,\Delta )$ by I. Kolář.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {general connection; linear connection; classical linear connection; vertical parallelism; natural operators; general connection; linear connection; classical linear connection; vertical parallelism; natural operators},
language = {eng},
number = {4},
pages = {223-240},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the Kolář connection},
url = {http://eudml.org/doc/260831},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - On the Kolář connection
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 4
SP - 223
EP - 240
AB - Let $Y\rightarrow M$ be a fibred manifold with $m$-dimensional base and $n$-dimensional fibres and $E\rightarrow M$ be a vector bundle with the same base $M$ and with $n$-dimensional fibres (the same $n$). If $m\ge 2$ and $n\ge 3$, we classify all canonical constructions of a classical linear connection $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ on $Y$ from a system $(\Gamma ,\Lambda ,\Phi ,\Delta )$ consisting of a general connection $\Gamma $ on $Y\rightarrow M$, a torsion free classical linear connection $\Lambda $ on $M$, a vertical parallelism $\Phi \colon Y\times _ME\rightarrow VY$ on $Y$ and a linear connection $\Delta $ on $E\rightarrow M$. An example of such $A(\Gamma ,\Lambda ,\Phi ,\Delta )$ is the connection $(\Gamma ,\Lambda ,\Phi ,\Delta )$ by I. Kolář.
LA - eng
KW - general connection; linear connection; classical linear connection; vertical parallelism; natural operators; general connection; linear connection; classical linear connection; vertical parallelism; natural operators
UR - http://eudml.org/doc/260831
ER -