Abstract
Let ? ? 2 be a fixed natural number. The complete description is given of the product preserving gauge bundle functors F on the category F?VB of flag vector bundles K = (K;K1,...,K?) of length ? in terms of the systems I = (I1,..., I??1) of A-module homomorphisms Ii : Vi+1 ? Vi for Weil algebras A and finite dimensional (over R) A-modules V1,...,V?. The so called iteration problem is investigated. The natural affinors on FK are classified. The gauge-natural operators C lifting ?-flag-linear (i.e. with the flow in F?VB) vector fields X on K to vector fields C(X) on FK are completely described. The concept of the complete lift F ? of a ?-flag-linear semi-basic tangent valued p-form ? on K is introduced. That the complete lift F ? preserves the Fr?licher-Nijenhuis bracket is deduced. The obtained results are applied to study prolongation and torsion of ?-flag-linear connections.
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