Displaying similar documents to “On the Lie algebra of vertical prolongation operators”

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.

Prolongation of projectable tangent valued forms

Antonella Cabras, Ivan Kolář (2002)

Archivum Mathematicum

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First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.