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The natural affinors on the r-jet prolongations of a vector bundle

Mikulski W. M.

Demonstratio Mathematica

2004

Vol. 37, nr 3

709--717

Natural operators lifting projectable-projectable vector fields to product preserving bundle functors on fibered-fibered manifolds

Mikulski W. M., Tomáš J. M.

Demonstratio Mathematica

2004

Vol. 37, nr 3

697--707

For any product-preserving bundle functor F denned on the category F2 M of fibered-fibered manifolds, we determine all natural operators transforming projectable-projectable vector fields on Y 6 Ob(F2M) to vector fields on FY. We also determine all natural affinors on FY and prove a composition property analogous to that concerning Weil bundles.

Horizontal extension of connections into (2)-connections

Doupovec M., Mikulski W. M.

Demonstratio Mathematica

2004

Vol. 37, nr 4

963--975

We discuss the prolongation of connections to to some non product preserving bundles. We introduce the concept of (r)-connection on a fibered manifold Y and for a given connection F on Y we construct its horizontal extension F(2). We also prove that F(2 ) is the unique (2)-connection on Y canonically dependent on F.

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 the contact (k, r)-coelements

Mikulski W. M.

Demonstratio Mathematica

2003

Vol. 36, nr 2

433--449

On some natural operators in vector fields

Mikulski W. M.

Demonstratio Mathematica

2003

Vol. 36, nr 1

221--230