Regularity conditions for liftings of functions and vector fields to natural bundles

Włodzimierz M. Mikulski

Displaying similar documents to “Regularity conditions for liftings of functions and vector fields to natural bundles”

Natural operators lifting functions to bundle functors on fibered manifolds

Włodzimierz M. Mikulski (1998)

Archivum Mathematicum

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The complete description of all natural operators lifting real valued functions to bundle functors on fibered manifolds is given. The full collection of all natural operators lifting projectable real valued functions to bundle functors on fibered manifolds is presented.

Natural transformations transforming functions and vector fields to functions on some natural bundles

Włodzimierz M. Mikulski (1992)

Mathematica Bohemica

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A classification of natural transformations transforming functions (or vector fields) to functions on such natural bundles which are restrictions of bundle functors is given.

Continuity of liftings

Włodzimierz M. Mikulski (1988)

Časopis pro pěstování matematiky

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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.