| Title:
|
Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles (English) |
| Author:
|
Dębecki, Jacek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
511-525 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 $T^A$. (English) |
| Keyword:
|
natural operator |
| Keyword:
|
Weil bundle |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 06604483 |
| idMR:
|
MR3519618 |
| DOI:
|
10.1007/s10587-016-0272-z |
| . |
| Date available:
|
2016-06-16T12:59:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145740 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
