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

Jacek Dębecki

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 511-525
  • ISSN: 0011-4642

Abstract

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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 A M , where T A is a Weil bundle, under the condition that p ≥ 1 , n ≥ p and n ≥ 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 .

How to cite

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Dębecki, Jacek. "Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles." Czechoslovak Mathematical Journal 66.2 (2016): 511-525. <http://eudml.org/doc/280099>.

@article{Dębecki2016,
abstract = {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 $T^A$.},
author = {Dębecki, Jacek},
journal = {Czechoslovak Mathematical Journal},
keywords = {natural operator; Weil bundle},
language = {eng},
number = {2},
pages = {511-525},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles},
url = {http://eudml.org/doc/280099},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Dębecki, Jacek
TI - Linear natural operators lifting $p$-vectors to tensors of type $(q,0)$ on Weil bundles
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 511
EP - 525
AB - 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 $T^A$.
LA - eng
KW - natural operator; Weil bundle
UR - http://eudml.org/doc/280099
ER -

References

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  7. Kol{á}{ř}, I., 10.1007/BF00133034, Ann. Global Anal. Geom. 6 (1988), 109-117. (1988) Zbl0678.58003MR0982760DOI10.1007/BF00133034
  8. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, (corrected electronic version) Springer, Berlin (1993). (1993) MR1202431
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  10. Mikulski, W. M., The linear natural operators lifting 2-vector fields to some Weil bundles, Note Mat. 19 (1999), 213-217. (1999) Zbl1008.58004MR1816875

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