Lifting of projectable vector fields to vertical fiber product preserving vector bundles

Włodzimierz M. Mikulski

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On the natural operators transforming vector fields to the $r$ -th tensor power

Kolář, Ivan

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Natural operations on higher order tangent bundles.

Ivan Kolár (1996)

Extracta Mathematicae

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We present a survey of some recent results about natural operations on the r-th order tangent bundle and similar objects.

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.

Displaying similar documents to “Lifting of projectable vector fields to vertical fiber product preserving vector bundles”

On the natural operators transforming vector fields to the r -th tensor power

Natural operations on higher order tangent bundles.

Prolongation of vector fields to jet bundles

On the natural operators transforming vector fields to the $r$ -th tensor power