| Title:
|
Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles (English) |
| Author:
|
Dębecki, Jacek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
933-943 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper contains a classification of linear liftings of skew symmetric tensor fields of type $(1,2)$ on $n$-dimensional manifolds to tensor fields of type $(1,2)$ on Weil bundles under the condition that $n\ge 3.$ It complements author's paper ``Linear liftings of symmetric tensor fields of type $(1,2)$ to Weil bundles'' (Ann. Polon. Math. {\it 92}, 2007, pp. 13--27), where similar liftings of symmetric tensor fields were studied. We apply this result to generalize that of author's paper ``Affine liftings of torsion-free connections to Weil bundles'' (Colloq. Math. {\it 114}, 2009, pp. 1--8) and get a classification of affine liftings of all linear connections to Weil bundles. (English) |
| Keyword:
|
natural operator |
| Keyword:
|
Weil bundle |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1224.58004 |
| idMR:
|
MR2738957 |
| . |
| Date available:
|
2010-11-20T13:53:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140794 |
| . |
| Reference:
|
[1] Dębecki, J.: Linear liftings of skew-symmetric tensor fields to Weil bundles.Czech. Math. J. 55 (130) (2005), 809-816. MR 2153104, 10.1007/s10587-005-0067-0 |
| Reference:
|
[2] Dębecki, J.: Linear liftings of $p$-forms to $q$-forms on Weil bundles.Monatsh. Math. 148 (2006), 101-117. MR 2235358, 10.1007/s00605-005-0348-6 |
| Reference:
|
[3] Dębecki, J.: Linear liftings of symmetric tensor fields of type $(1,2)$ to Weil bundles.Ann. Polon. Math. 92 (2007), 13-27. MR 2318507, 10.4064/ap92-1-2 |
| Reference:
|
[4] Dębecki, J.: Affine liftings of torsion-free connections to Weil bundles.Colloq. Math. 114 (2009), 1-8. MR 2457274, 10.4064/cm114-1-1 |
| 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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| . |
