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Prolongation of tangent valued forms to Weil bundles. (English) Zbl 0843.53021
A tangent valued $$k$$-form $$P$$ on a smooth manifold $$M$$ is an antisymmetric tensor field of type $$(1,k)$$ on $$M$$. If $$Q$$ is a tangent valued $$\ell$$-form on $$M$$, the Fröhlicher-Nijenhuis bracket $$[P,Q ]$$ is a tangent valued $$(k+\ell)$$-form on $$M$$. The authors consider the complete liftings of tangent valued forms from a manifold $$M$$ to the Weil bundle $$M$$ associated to a Weil algebra $$A$$ and prove that the complete lifts preserve the Fröhlicher-Nijenhuis brackets.

##### MSC:
 53C05 Connections (general theory) 58A20 Jets in global analysis
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