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

Włodzimierz M. Mikulski

Displaying similar documents to “Natural transformations transforming functions and vector fields to functions on 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 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 liftings of vector fields to tangent bundles of bundles of $1$ -forms

Piotr Kobak (1991)

Mathematica Bohemica

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Natural liftings $D : I \to I T T^{*}$ are classified for $n \geq 2$ . It is proved that they form a 5-parameter family of operators.

Lifting of projectable vector fields to vertical fiber product preserving vector bundles

Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

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We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.

Displaying similar documents to “Natural transformations transforming functions and vector fields to functions on some natural bundles”

On the Weilian prolongations of natural bundles

Natural differential operators between some natural bundles

Natural liftings of vector fields to tangent bundles of bundles of 1 -forms

Lifting of projectable vector fields to vertical fiber product preserving vector bundles

Natural liftings of vector fields to tangent bundles of bundles of $1$ -forms