Displaying similar documents to “Natural lifting of connections to vertical bundles”

On the existence of prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Czechoslovak Mathematical Journal

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We classify all bundle functors G admitting natural operators transforming connections on a fibered manifold Y → M into connections on G Y → M . Then we solve a similar problem for natural operators transforming connections on Y → M into connections on G Y → Y .

Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec, Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

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Let F be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the F -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to F -vertical bundles. We also present some examples and applications.

Prolongation of vector fields to jet bundles

Kolář, Ivan, Slovák, Jan

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[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation J r Y are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.