Liftings of linear vector fields to product preserving gauge bundle functors on vector bundles.

Kureš, Miroslav; Mikulski, Włodzimierz M.

Displaying similar documents to “Liftings of linear vector fields to product preserving gauge bundle functors on vector bundles.”

Some further results on lifts of linear vector fields related to product preserving gauge bundle functors on vector bundles

A. Ntyam, G. F. Wankap Nono, Bitjong Ndombol (2016)

Archivum Mathematicum

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We present some lifts (associated to a product preserving gauge bundle functor on vector bundles) of sections of the dual bundle of a vector bundle, some derivations and linear connections on vector bundles.

The natural affinors on some fiber product preserving gauge bundle functors of vector bundles

Jan Kurek, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

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We classify all natural affinors on vertical fiber product preserving gauge bundle functors $F$ on vector bundles. We explain this result for some more known such $F$ . We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor $F^{*}$ dual to $F$ as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.

On lifts of some projectable vector fields associated to a product preserving gauge bundle functor on vector bundles

A. Ntyam, G. F. Wankap Nono, Bitjong Ndombol (2014)

Archivum Mathematicum

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For a product preserving gauge bundle functor on vector bundles, we present some lifts of smooth functions that are constant or linear on fibers, and some lifts of projectable vector fields that are vector bundle morphisms.

Product preserving gauge bundle functors on all principal bundle homomorphisms

Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means...

Natural transformations transforming functions and vector fields to functions on some natural bundles

Włodzimierz M. Mikulski (1992)

Mathematica Bohemica

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A classification of natural transformations transforming functions (or vector fields) to functions on such natural bundles which are restrictions of bundle functors is given.

On the Weilian prolongations of natural bundles

Ivan Kolář (2012)

Czechoslovak Mathematical Journal

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We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration $F (E M)$ of two natural bundles $E$ and $F$ . Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.