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A construction of a connection on G Y Y from a connection on Y M by means of classical linear connections on M and Y

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

Let G be a bundle functor of order ( r , s , q ) , s r q , on the category m , n of ( m , n ) -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection Γ on an m , n -object Y M we construct a general connection 𝒢 ( Γ , λ , Λ ) on G Y Y be means of an auxiliary q -th order linear connection λ on M and an s -th order linear connection Λ on Y . Then we construct a general connection 𝒢 ( Γ , 1 , 2 ) on G Y Y by means of auxiliary classical linear connections 1 on M and 2 on Y . In the case G = J 1 we determine all general connections 𝒟 ( Γ , ) on J 1 Y Y from...

A generalization of the exterior product of differential forms combining Hom-valued forms

Christian Gross (1997)

Commentationes Mathematicae Universitatis Carolinae

This article deals with vector valued differential forms on C -manifolds. As a generalization of the exterior product, we introduce an operator that combines Hom ( s ( W ) , Z ) -valued forms with Hom ( s ( V ) , W ) -valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.

Champs de vecteurs et formes différentielles sur une variété des points proches

Basile Guy Richard Bossoto, Eugène Okassa (2008)

Archivum Mathematicum

Let M be a smooth manifold, A a local algebra in sense of André Weil, M A the manifold of near points on M of kind A and 𝔛 ( M A ) the module of vector fields on M A . We give a new definition of vector fields on M A and we show that 𝔛 ( M A ) is a Lie algebra over A . We study the cohomology of A -differential forms. Résumé. On considère M une variété différentielle, A une algèbre locale au sens d’André Weil, M A la variété des points proches de M d’espèce A et 𝔛 ( M A ) le module des champs de vecteurs sur M A . On donne une nouvelle...

Constructions on second order connections

J. Kurek, W. M. Mikulski (2007)

Annales Polonici Mathematici

We classify all m , n -natural operators : J ² J ² V A transforming second order connections Γ: Y → J²Y on a fibred manifold Y → M into second order connections ( Γ ) : V A Y J ² V A Y on the vertical Weil bundle V A Y M corresponding to a Weil algebra A.

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