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

Czechoslovak Mathematical Journal

Jacek ²  Dbecki³ 

[1] 6, 30-348 Kraków, Poland;Instytut Matematyki Uniwersytetu Jagiellońskiego, ul. ojasiewicza 

关键词: natural operator;    Weil bundle;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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 $p\ge1$, $n\ge p$ 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 $T^A$.

【 授权许可】

Unknown