Some natural operations between connections on fibred manifolds

Doupovec, Miroslav; Vondra, Alexandr

Displaying similar documents to “Some natural operations between connections on fibred manifolds”

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...

On the connections naturally induced on the second order frame bundle

Josef Janyška, Ivan Kolář (1986)

Archivum Mathematicum

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Prolongation of second order connections to vertical Weil bundles

Antonella Cabras, Ivan Kolář (2001)

Archivum Mathematicum

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We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$ . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$ -field for another Weil algebra $B$ and of its $A$ -prolongation.

Higher order Cartan connections

Juraj Virsik (1996)

Archivum Mathematicum

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A Cartan connection associated with a pair $P (M, G^{'}) \subset P (M, G)$ is defined in the usual manner except that only the injectivity of $ω : T (P^{'}) \to T {(G)}_{e}$ is required. For an $r$ -th order connection associated with a bundle morphism $Φ : P^{'} \to P$ the concept of Cartan order $q \leq r$ is defined, which for $q = r = 1, Φ : P^{'} \subset P$ , and $dim M = dim G / G^{'}$ coincides with the classical definition. Results are obtained concerning the Cartan order of $r$ -th order connections that are the product of $r$ first order (Cartan) connections.