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Soldered double linear morphisms

Alena Vanžurová (1992)

Mathematica Bohemica

Our aim is to show a method of finding all natural transformations of a functor T T * into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps f : C 0 → C 0 commuting with T T * -soldered automorphisms of a double vector space C 0 = V * × V × V * are investigated. On the set Z s ( C 0 ) of such mappings, appropriate partial operations are introduced. The natural transformations T T * → T T * are bijectively related with the elements...

Some aspects of the homogeneous formalism in field theory and gauge invariance

Marcella Palese, Ekkehart Winterroth (2006)

Archivum Mathematicum

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version of the Hilbert–Einstein...

Some functorial prolongations of general connections

Ivan Kolář (2018)

Archivum Mathematicum

We consider the problem of prolongating general connections on arbitrary fibered manifolds with respect to a product preserving bundle functor. Our main tools are the theory of Weil algebras and the Frölicher-Nijenhuis bracket.

Some geometric aspects of the calculus of variations in several independent variables

David Saunders (2010)

Communications in Mathematics

This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.

Some natural operators on vector fields

Jiří M. Tomáš (1995)

Archivum Mathematicum

We determine all natural operators transforming vector fields on a manifold M to vector fields on T * T 1 2 M , dim M ≥ 2 , and all natural operators transforming vector fields on M to functions on T * T T 1 2 M , dim M ≥ 3 . We describe some relations between these two kinds of natural operators.

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second, the tempered-stratified...

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