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The natural affinors on the r-th order frame bundle

Kurek J., Mikulski W.

Demonstratio Mathematica

2008

Vol. 41, nr 3

701-704

Some natural operations on functions

Mikulski W.

Demonstratio Mathematica

2007

Vol. 40, nr 3

745-749

Let F : FMm &rarr FM be a bundle functor. We describe all FMm,n- natural operators L transforming functions f : Y &rarr R, Y is an element of Obj(FMm,n), into functions L(f) : FY &rarr R.

Bundles of contact elements on fibered fibered manifolds and the flow operator

Mikulski W., Tomas J.

Demonstratio Mathematica

2007

Vol. 40, nr 2

485-493

We define the concept of a fibered fibered (k1, k2, l1, l2)- contact element of order (r1, . . . , r8) for r8 > r4 < r5 > r3, r8 > r6 < r7 > r2 and r1 < ri for ri = 2, 3, . . . , 8. For k1 < m1, k2 < m2, l1 < n1, l2 < n2, we define a bundle func tor Kr1,...,r8/ k1,k2,l1,l2 defined on the category FM2 m1,m2,n1,n2 of (m1,m2, n1,n2)-fibere fibered manifolds. We prove that the only natural transformation on the bundle functor Kr1,...r8/ k1,k2,l1,l2 is the identity one. Moreover, we prove that any natural operator lifting projectable vector fields Y to Kr1,...r8/ k1,k2,l1,l2 Y is a constant multiple of the flow operator.

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.

Lifting of vector fields to 1-forms on r-jet prolongation of the bundle of tensors of type (0,2)

Michalec P.

Demonstratio Mathematica

2006

Vol. 39, nr 2

471-481

For natural numbers n > 2 and r > 1 all natural operators T* (Jr(*2T*)) lifting vector fields from n-manifolds M into 1-forms on Jr(*2T*) are classified. It's proved that the set of all natural operators A.

Corrrection of the proof of lemma 7 of the paper " Horizontal extension of connections into (2)-connections", Demonstratio Math. XXXVII (4) (2004), 963-975

Doupovec M., Mikulski W.

Demonstratio Mathematica

2006

Vol. 39, nr 3

729-730

We correct the mistake in the proof of Lemma 7 in our paper "Horizontal extension of connections into (2)-connections" published in Demonstratio Math. XXXVII (4) (2004).

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.