Displaying similar documents to “Higher order jet involution”

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...

Prolongation of second order connections to vertical Weil bundles

Antonella Cabras, Ivan Kolář (2001)

Archivum Mathematicum

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We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra A . In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a B -field for another Weil algebra B and of its A -prolongation.

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 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 .