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Negative answers to some questions about constructions on connections

Mikulski W.

Demonstratio Mathematica

2006

Vol. 39, nr 3

685-689

Let m and n be natural numbers. For an arbitrary bundle functor G on the category FMm,n of fibred manifolds with m-dimensional bases and n-dimensional fibers and their local fibered diffeomorphisms we prove that there is no FMm,n-natural operator V transforming general connections.

There exists a bundle functor of jet bundle type of infinite order in the first factor

Mikulski W.

Demonstratio Mathematica

2005

Vol. 38, nr 4

961--964

It is known a complete description of all bundle functors on Mfm x Mf of finite order in the first factor. The most known example of such a bundle functor is the r-jet bundle functor Jr on Mfm x Mf. In the present note an example of a bundle functor on Mfm x Mf of (essentially) infinite order in the first factor is constructed.

Liftings of projectable vector fields to 1-forms on higher order contangent bundles over fibered manifolds

Mikulski W., Tomáš J. M.

Demonstratio Mathematica

2004

Vol. 37, nr 2

447--462

On the contact (k, r)-coelements

Mikulski W. M.

Demonstratio Mathematica

2003

Vol. 36, nr 2

433--449