Natural differential operators between some natural bundles

Włodzimierz M. Mikulski

Displaying similar documents to “Natural differential operators between some natural bundles”

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.

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 $n \geq q$ .

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.

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...