Displaying similar documents to “The natural functions on the cotangent bundle of higher order vector tangent bundles over fibered manifolds”

Non-holonomic ( r , s , q ) -jets

Jiří M. Tomáš (2006)

Czechoslovak Mathematical Journal

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We generalize the concept of an ( r , s , q ) -jet to the concept of a non-holonomic ( r , s , q ) -jet. We define the composition of such objects and introduce a bundle functor J ˜ r , s , q ℱ ℳ k , l × ℱ ℳ defined on the product category of ( k , l ) -dimensional fibered manifolds with local fibered isomorphisms and the category of fibered manifolds with fibered maps. We give the description of such functors from the point of view of the theory of Weil functors. Further, we introduce a bundle functor J ˜ 1 r , s , q 2 - ℱ ℳ k , l → ℱ ℳ defined on the category of 2 -fibered manifolds...

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. ...

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.

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 → M into connections on G Y → M . Then we solve a similar problem for natural operators transforming connections on Y → M into connections on G Y → Y .