Higher order Cartan connections

Juraj Virsik

Displaying similar documents to “Higher order Cartan connections”

Some natural operations between connections on fibred manifolds

Doupovec, Miroslav, Vondra, Alexandr

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Given a fibered manifold $Y \to X$ , a 2-connection on $Y$ means a section $J^{1} Y \to J^{2} Y$ . The authors determine all first order natural operators transforming a 2-connection on $Y$ and a classical linear connection on $X$ into a connection on $J^{1} Y \to Y$ . (The proof implies that there is no first order natural operator transforming 2-connections on $Y$ into connections on $J^{1} Y \to Y$ .) Using this result, the authors deduce several properties of characterizable connections on $J^{1} Y \to X$ .

Second order connections on some functional bundles

Antonella Cabras, Ivan Kolář (1999)

Archivum Mathematicum

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We study the second order connections in the sense of C. Ehresmann. On a fibered manifold $Y$ , such a connection is a section from $Y$ into the second non-holonomic jet prolongation of $Y$ . Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on $Y$ , which are deduced in the first part of...

Total connections in Lie groupoids

Juraj Virsik (1995)

Archivum Mathematicum

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A total connection of order $r$ in a Lie groupoid $Φ$ over $M$ is defined as a first order connections in the $(r - 1)$ -st jet prolongations of $Φ$ . A connection in the groupoid $Φ$ together with a linear connection on its base, ie. in the groupoid $Π (M)$ , 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 $Φ$ defines a total reduction of the $r$ -th prolongation...

Connections on higher order principal prolongations

Vašík, Petr

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Geometric constructions of connections on the higher order principal prolongations of a principal bundle are considered. Moreover, the existing differences among connections on non-holonomic, semiholonomic and holonomic principal prolongations are discussed.