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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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