Linear liftings of skew symmetric tensor fields of type ( 1 , 2 ) to Weil bundles

Jacek Dębecki

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 933-943
  • ISSN: 0011-4642

Abstract

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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 ≥ 3 . It complements author’s paper “Linear liftings of symmetric tensor fields of type ( 1 , 2 ) to Weil bundles” (Ann. Polon. Math. 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. 114, 2009, pp. 1–8) and get a classification of affine liftings of all linear connections to Weil bundles.

How to cite

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Dębecki, Jacek. "Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles." Czechoslovak Mathematical Journal 60.4 (2010): 933-943. <http://eudml.org/doc/196567>.

@article{Dębecki2010,
abstract = {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. 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. 114, 2009, pp. 1–8) and get a classification of affine liftings of all linear connections to Weil bundles.},
author = {Dębecki, Jacek},
journal = {Czechoslovak Mathematical Journal},
keywords = {natural operator; Weil bundle; natural operator; Weil bundle},
language = {eng},
number = {4},
pages = {933-943},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles},
url = {http://eudml.org/doc/196567},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Dębecki, Jacek
TI - Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 933
EP - 943
AB - 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. 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. 114, 2009, pp. 1–8) and get a classification of affine liftings of all linear connections to Weil bundles.
LA - eng
KW - natural operator; Weil bundle; natural operator; Weil bundle
UR - http://eudml.org/doc/196567
ER -

References

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  1. Dębecki, J., 10.1007/s10587-005-0067-0, Czech. Math. J. 55 (130) (2005), 809-816. (2005) MR2153104DOI10.1007/s10587-005-0067-0
  2. Dębecki, J., 10.1007/s00605-005-0348-6, Monatsh. Math. 148 (2006), 101-117. (2006) MR2235358DOI10.1007/s00605-005-0348-6
  3. Dębecki, J., 10.4064/ap92-1-2, Ann. Polon. Math. 92 (2007), 13-27. (2007) MR2318507DOI10.4064/ap92-1-2
  4. Dębecki, J., 10.4064/cm114-1-1, Colloq. Math. 114 (2009), 1-8. (2009) MR2457274DOI10.4064/cm114-1-1
  5. Doupovec, M., Mikulski, W. M., 10.1007/s10587-006-0096-3, Czech. Math. J. 56 (131) (2006), 1323-1334. (2006) Zbl1164.58300MR2280811DOI10.1007/s10587-006-0096-3
  6. Eck, D. J., 10.1016/0022-4049(86)90076-9, J. Pure Appl. Algebra 42 (1986), 133-140. (1986) Zbl0615.57019MR0857563DOI10.1016/0022-4049(86)90076-9
  7. Gancarzewicz, J., Mikulski, W., Pogoda, Z., 10.1017/S0027763000004931, Nagoya Math. J. 135 (1994), 1-41. (1994) Zbl0813.53010MR1295815DOI10.1017/S0027763000004931
  8. Kainz, G., Michor, P., Natural transformations in differential geometry, Czech. Math. J. 37 (112) (1987), 584-607. (1987) Zbl0654.58001MR0913992
  9. Kolář, I., 10.1007/BF00133034, Ann. Global Anal. Geom. 6 (1988), 109-117. (1988) MR0982760DOI10.1007/BF00133034
  10. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag Berlin (1993). (1993) MR1202431
  11. Kurek, J., Mikulski, W. M., Canonical symplectic structures on the r th order tangent bundle of a symplectic manifold, Extr. Math. 21 (2006), 159-166. (2006) Zbl1141.58002MR2292745
  12. Luciano, O., 10.1017/S0027763000002774, Nagoya Math. J. 109 (1988), 69-89. (1988) Zbl0661.58007MR0931952DOI10.1017/S0027763000002774
  13. Mikulski, W. M., 10.1017/S0027763000005444, Nagoya Math. J. 140 (1995), 117-137. (1995) Zbl0854.53018MR1369482DOI10.1017/S0027763000005444
  14. Morimoto, A., 10.4310/jdg/1214433720, J. Diff. Geom. 11 (1976), 479-498. (1976) MR0445422DOI10.4310/jdg/1214433720
  15. Weil, A., Théorie des points proches sur les variétés différentielles, Colloques Internat. Centre Nat. Rech. Sci. 52 (1953), 111-117 French. (1953) MR0061455

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