On principal connection like bundles

Włodzimierz M. Mikulski

Displaying similar documents to “On principal connection like bundles”

Non-existence of natural operators transforming connections on $Y \to M$ into connections on $F Y \to Y$

Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

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Under some weak assumptions on a bundle functor $F : F M_{m, n} \to F M$ we prove that there is no $F M_{m, n}$ -natural operator transforming connections on $Y \to M$ into connections on $F Y \to Y$ .

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 the fiber product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2003)

Annales Polonici Mathematici

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We present a complete description of all fiber product preserving gauge bundle functors F on the category $_{m}$ of vector bundles with m-dimensional bases and vector bundle maps with local diffeomorphisms as base maps. Some corollaries of this result are presented.

On the existence of prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Czechoslovak Mathematical Journal

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We classify all bundle functors $G$ admitting natural operators transforming connections on a fibered manifold $Y \to M$ into connections on $G Y \to M$ . Then we solve a similar problem for natural operators transforming connections on $Y \to M$ into connections on $G Y \to Y$ .

Product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2001)

Colloquium Mathematicae

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A complete description is given of all product preserving gauge bundle functors F on vector bundles in terms of pairs (A,V) consisting of a Weil algebra A and an A-module V with $d i m_{ℝ} (V) < \infty$ . Some applications of this result are presented.

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.

Displaying similar documents to “On principal connection like bundles”

Non-existence of natural operators transforming connections on Y → M into connections on F Y → Y

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

On the fiber product preserving gauge bundle functors on vector bundles

On the existence of prolongation of connections

Product preserving gauge bundle functors on vector bundles

On the Weilian prolongations of natural bundles

Non-existence of natural operators transforming connections on $Y \to M$ into connections on $F Y \to Y$