Displaying similar documents to “Product preserving bundles on foliated manifolds”

Some functorial prolongations of general connections

Ivan Kolář (2018)

Archivum Mathematicum

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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.

Product preserving bundle functors on fibered manifolds

Włodzimierz M. Mikulski (1996)

Archivum Mathematicum

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The complete description of all product preserving bundle functors on fibered manifolds in terms of natural transformations between product preserving bundle functors on manifolds is given.

Product preserving bundle functors on fibered fibered manifolds

Włodzimierz M. Mikulski, Jiří M. Tomáš (2003)

Colloquium Mathematicae

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We investigate the category of product preserving bundle functors defined on the category of fibered fibered manifolds. We show a bijective correspondence between this category and a certain category of commutative diagrams on product preserving bundle functors defined on the category ℳ f of smooth manifolds. By an application of the theory of Weil functors, the latter category is considered as a category of commutative diagrams on Weil algebras. We also mention the relation with natural...

On infinitesimal automorphisms of foliated manifolds

Jan Kurek, Włodzimierz M. Mikulski (2007)

Annales Polonici Mathematici

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Let F:ℱol → ℱℳ be a product preserving bundle functor on the category ℱol of foliated manifolds (M,ℱ) without singularities and leaf respecting maps. We describe all natural operators C transforming infinitesimal automorphisms X ∈ 𝒳(M,ℱ) of foliated manifolds (M,ℱ) into vector fields C(X)∈ 𝒳(F(M,ℱ)) on F(M,ℱ).

Natural transformations of the covelocities functors into some natural bundles

Włodzimierz M. Mikulski (1993)

Mathematica Bohemica

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In this paper are determined all natural transformations of the natural bundle of ( g , r ) -covelocities over n -manifolds into such a linear natural bundle over n -manifolds which is dual to the restriction of a linear bundle functor, if n ≥ q .