Canonical vector valued 1-forms on higher order adapted frame bundles over category of fibered squares

Anna Bednarska

Displaying similar documents to “Canonical vector valued 1-forms on higher order adapted frame bundles over category of fibered squares”

Connection theory on differentiable fibre bundles: A concise introduction.

Iliev, Bozhidar Z. (2006)

International Journal of Mathematics and Mathematical Sciences

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Natural affinors on the r -th order adapted frame bundle over fibered-fibered manifolds

Agnieszka Czarnota (2008)

Annales UMCS, Mathematica

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We describe all F2Mm1,m2,n1,n2-natural affinors on the r-th order adapted frame bundle PrAY over (m1,m2, n1, n2)-dimensional fibered-fibered manifolds Y.

Prolongation of projectable tangent valued forms

Antonella Cabras, Ivan Kolář (2002)

Archivum Mathematicum

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First we deduce some general properties of product preserving bundle functors on the category of fibered manifolds. Then we study the prolongation of projectable tangent valued forms with respect to these functors and describe the complete lift of the Frölicher-Nijenhuis bracket. We also present the coordinate formula for composition of semiholonomic jets.

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 affinors on time-dependent Weil bundles

Miroslav Doupovec, Ivan Kolář (1991)

Archivum Mathematicum

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Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold.

Janyška, J., Modugno, M. (1996)

Archivum Mathematicum

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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. ...