A general point of view to nonholonomic jet bundles

Ivan Kolár

Displaying similar documents to “A general point of view to nonholonomic jet bundles”

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 $G Y \to Y$ .

On involutions of iterated bundle functors

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Colloquium Mathematicae

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We introduce the concept of an involution of iterated bundle functors. Then we study the problem of the existence of an involution for bundle functors defined on the category of fibered manifolds with m-dimensional bases and of fibered manifold morphisms covering local diffeomorphisms. We also apply our results to prolongation of connections.

Fiber product preserving bundle functors on all morphisms of fibered manifolds

Ivan Kolář, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

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We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of $r$ -jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.

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. ...