# Article

MSC: 58A32
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Keywords:
natural operator; Weil bundle
Summary:
We give a classification of all linear natural operators transforming \$p\$-vectors (i.e., skew-symmetric tensor fields of type \$(p,0)\$) on \$n\$-dimensional manifolds \$M\$ to tensor fields of type \$(q,0)\$ on \$T^AM\$, where \$T^A\$ is a Weil bundle, under the condition that \$p\ge 1\$, \$n\ge p\$ and \$n\ge q\$. The main result of the paper states that, roughly speaking, each linear natural operator lifting \$p\$-vectors to tensor fields of type \$(q,0)\$ on \$T^A\$ is a sum of operators obtained by permuting the indices of the tensor products of linear natural operators lifting \$p\$-vectors to tensor fields of type \$(p,0)\$ on \$T^A\$ and canonical tensor fields of type \$(q-p,0)\$ on \$T^A\$.
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