Displaying similar documents to “On special types of semiholonomic 3 -jets”

Natural affinors on ( J r , s , q ( . , 1 , 1 ) 0 ) *

Włodzimierz M. Mikulski (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let r , s , q , m , n be such that s r q . Let Y be a fibered manifold with m -dimensional basis and n -dimensional fibers. All natural affinors on ( J r , s , q ( Y , 1 , 1 ) 0 ) * are classified. It is deduced that there is no natural generalized connection on ( J r , s , q ( Y , 1 , 1 ) 0 ) * . Similar problems with ( J r , s ( Y , ) 0 ) * instead of ( J r , s , q ( Y , 1 , 1 ) 0 ) * are solved.

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 k , l × 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 - k , l 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. ...