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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

Natural liftings of connections to the r-th order bundle

Mikulski W.

Demonstratio Mathematica

2007

Vol. 40, nr 2

481-484

We describe all natural operators A lifting a clasiccal linear connection on an m-dimensional manifold M into a classical linear conection A() on the r-th order frame bundle LrM = invJr/0 (Rm,M).

The natural bundles admitting natural lifting of linear connections

Mikulski W.

Demonstratio Mathematica

2006

Vol. 39, nr 1

223-232

Natural bundles admitting natural lifting of linear connections are characterized. Corollaries are presented. Some other similar results are obtained, too.

The natural linear operators Λp T* → TTr*

Mikulski W. M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 1

127--136

For integers p ≥ 0, n ≥ p+2 and r ≥ 1 all natural linear operators Λp T*|Mfn → TTr* transforming p-forms from n-manifolds M into vector fields on the r-th order cotangent bundle Tr* M = Jr (M, R)0 of M are completely described.

On some natural operators in vector fields

Mikulski W. M.

Demonstratio Mathematica

2003

Vol. 36, nr 1

221--230

Liftings of vector fields to (JrT*,a)

Mikulski W.

Demonstratio Mathematica

2002

Vol. 35, nr 1

211-216