Natural liftings of vector fields to tangent bundles of bundles of $1$-forms

Piotr Kobak

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Displaying similar documents to “Natural liftings of vector fields to tangent bundles of bundles of $1$ -forms”

On cotangent bundles of some natural bundles

Kolář, Ivan

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The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle $F$ ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of $F$ . It is deduced that under certain assumptions on $F$ , all natural operators of the second type can be constructed through those of the first one.

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 “Natural liftings of vector fields to tangent bundles of bundles of 1 -forms”

On cotangent bundles of some natural bundles

Prolongation of vector fields to jet bundles

Displaying similar documents to “Natural liftings of vector fields to tangent bundles of bundles of $1$ -forms”