Natural operations on higher order tangent bundles.
Ivan Kolár (1996)
Extracta Mathematicae
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We present a survey of some recent results about natural operations on the r-th order tangent bundle and similar objects.
Ivan Kolár (1996)
Extracta Mathematicae
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We present a survey of some recent results about natural operations on the r-th order tangent bundle and similar objects.
Kolář, Ivan, Slovák, Jan
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[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.
Kolář, Ivan
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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 on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold into connections on an arbitrary vertical bundle over . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over under which every natural operator in question has finite order. ...