Displaying similar documents to “Symmetries of connections on fibered manifolds”

Some natural operations between connections on fibred manifolds

Doupovec, Miroslav, Vondra, Alexandr

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Given a fibered manifold Y → X , a 2-connection on Y means a section J 1 Y → 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 → Y . (The proof implies that there is no first order natural operator transforming 2-connections on Y into connections on J 1 Y → Y .) Using this result, the authors deduce several properties of characterizable connections on J 1 Y → X .

On the iterated absolute differentiation on some functional bundles

Antonella Cabras, Ivan Kolář (1997)

Archivum Mathematicum

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We deduce further properties of connections on the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base, which we introduced in [2]. In particular, we define the vertical prolongation of such a connection, discuss the iterated absolute differentiation by means of an auxiliary linear connection on the base manifold and prove the general Ricci identity.