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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.

O analizie tensorowej czyli o pochodnej kowariantnej

Kordecki Z.

Czasopismo Techniczne. Środowisko

2003

R. 100, z. 1-Ś

103--120

This paper outlines the origin of the notion of the covariant derivative of the tensor field. What has been particularly emphasised are the conditions and causes of the fact that the notion "the ordinary R3 derivative" has become inadequate, since it does not produce a tensor nor its field. The work has been based on original sources, as well as on references which give a currrent view on the question. What has been taken into consideration is the lack of equivalence between covariant and contravariant representations of a vector, with reference to the problem of the derivative of the vector field.

On tensor products in concrete categories

Pop I.

Demonstratio Mathematica

2000

Vol. 33, nr 4

707-718

In this paper we consider the notion of tensor product in a concrete category, in the sense of [5]. For such a tensor product, which we refer as a concrete tensor product we study some important properties: commutativity, associativity, epifunctoriality and zero object. We also consider examples and some special properties of tensor products and of concrete categories with tensor products for: arbitrary topological spaces, compact spaces, left modules, right H-comodules and left H-modules, for H a Hopf algebra.