Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles

Dębecki, Jacek

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 511-525.

Résumé

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 $T^{A}M$, 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 $T^A$.

Détail

DOI : 10.1007/s10587-016-0272-z

Classification : 58A32
Mots-clés : natural operator; Weil bundle