Geodesic
Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 511-525 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $T^A$.
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 $T^A$.
DOI : 10.1007/s10587-016-0272-z
Classification : 58A32
Keywords: natural operator; Weil bundle 
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     journal = {Czechoslovak Mathematical Journal},
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     year = {2016},
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Dębecki, Jacek. Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 511-525. doi: 10.1007/s10587-016-0272-z

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