On the Weilian prolongations of natural bundles

Ivan Kolář

Displaying similar documents to “On the Weilian prolongations of natural 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.

Natural differential operators between some natural bundles

Włodzimierz M. Mikulski (1993)

Mathematica Bohemica

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Let $F$ and $G$ be two natural bundles over $n$ -manifolds. We prove that if $F$ is of type (I) and $G$ is of type (II), then any natural differential operator of $F$ into $G$ is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles.

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 $n \geq q$ .

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.

Natural lifting of connections to vertical bundles

Kolář, Ivan, Mikulski, Włodzimierz M.

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One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order $(r, s, q)$ on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold $Y$ into connections on an arbitrary vertical bundle over $Y$ . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over $Y$ under which every natural operator in question has finite order. ...