Total connections in Lie groupoids

Virsik, Juraj. "Total connections in Lie groupoids." Archivum Mathematicum 031.3 (1995): 183-200. <http://eudml.org/doc/247691>.

@article{Virsik1995,
abstract = {A total connection of order $r$ in a Lie groupoid $\Phi $ over $M$ is defined as a first order connections in the $(r-1)$-st jet prolongations of $\Phi $. A connection in the groupoid $\Phi $ together with a linear connection on its base, ie. in the groupoid $\Pi (M)$, give rise to a total connection of order $r$, which is called simple. It is shown that this simple connection is curvature-free iff the generating connections are. Also, an $r$-th order total connection in $\Phi $ defines a total reduction of the $r$-th prolongation of $\Phi $ to $\Phi \times \Pi (M)$. It is shown that when $r>2$ then this total reduction of a simple connection is holonomic iff the generating connections are curvature free and the one on $M$ also torsion-free.},
author = {Virsik, Juraj},
journal = {Archivum Mathematicum},
keywords = {Lie groupoids; semi-holonomic jets; higher order connections; total connections; simple connections; simple connection; higher-order connections; Lie groupoid; total connection},
language = {eng},
number = {3},
pages = {183-200},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Total connections in Lie groupoids},
url = {http://eudml.org/doc/247691},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Virsik, Juraj
TI - Total connections in Lie groupoids
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 3
SP - 183
EP - 200
AB - A total connection of order $r$ in a Lie groupoid $\Phi $ over $M$ is defined as a first order connections in the $(r-1)$-st jet prolongations of $\Phi $. A connection in the groupoid $\Phi $ together with a linear connection on its base, ie. in the groupoid $\Pi (M)$, give rise to a total connection of order $r$, which is called simple. It is shown that this simple connection is curvature-free iff the generating connections are. Also, an $r$-th order total connection in $\Phi $ defines a total reduction of the $r$-th prolongation of $\Phi $ to $\Phi \times \Pi (M)$. It is shown that when $r>2$ then this total reduction of a simple connection is holonomic iff the generating connections are curvature free and the one on $M$ also torsion-free.
LA - eng
KW - Lie groupoids; semi-holonomic jets; higher order connections; total connections; simple connections; simple connection; higher-order connections; Lie groupoid; total connection
UR - http://eudml.org/doc/247691
ER -