Total connections in Lie groupoids
Virsik, Juraj
Archivum Mathematicum, Tome 031 (1995), p. 183-200 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1995-01-01
Classification:  53C05,  58A20 
@article{107539,
     author = {Juraj Virsik},
     title = {Total connections in Lie groupoids},
     journal = {Archivum Mathematicum},
     volume = {031},
     year = {1995},
     pages = {183-200},
     zbl = {0841.53024},
     mrnumber = {1368257},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107539}
}

Virsik, Juraj. Total connections in Lie groupoids. Archivum Mathematicum, Tome 031 (1995) pp. 183-200. http://gdmltest.u-ga.fr/item/107539/

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