Geodesic
Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 933-943 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $n\ge 3.$ 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.
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.
Classification : 58A32
Keywords: natural operator; Weil bundle 
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     title = {Linear liftings of skew symmetric tensor fields of type $(1,2)$ to {Weil} bundles},
     journal = {Czechoslovak Mathematical Journal},
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Dębecki, Jacek. Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 933-943. http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a3/

[1] Dębecki, J.: Linear liftings of skew-symmetric tensor fields to Weil bundles. Czech. Math. J. 55 (130) (2005), 809-816. | DOI | MR

[2] Dębecki, J.: Linear liftings of $p$-forms to $q$-forms on Weil bundles. Monatsh. Math. 148 (2006), 101-117. | DOI | MR

[3] Dębecki, J.: Linear liftings of symmetric tensor fields of type $(1,2)$ to Weil bundles. Ann. Polon. Math. 92 (2007), 13-27. | DOI | MR

[4] Dębecki, J.: Affine liftings of torsion-free connections to Weil bundles. Colloq. Math. 114 (2009), 1-8. | DOI | MR

[5] Doupovec, M., Mikulski, W. M.: On the existence of prolongation of connections. Czech. Math. J. 56 (131) (2006), 1323-1334. | DOI | MR | Zbl

[6] Eck, D. J.: Product-preserving functors on smooth manifolds. J. Pure Appl. Algebra 42 (1986), 133-140. | DOI | MR | Zbl

[7] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors. Nagoya Math. J. 135 (1994), 1-41. | DOI | MR | Zbl

[8] Kainz, G., Michor, P.: Natural transformations in differential geometry. Czech. Math. J. 37 (112) (1987), 584-607. | MR | Zbl

[9] Kolář, I.: On natural operators on vector fields. Ann. Global Anal. Geom. 6 (1988), 109-117. | DOI | MR

[10] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer-Verlag Berlin (1993). | MR

[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. | MR | Zbl

[12] Luciano, O.: Categories of multiplicative functors and Weil's infinitely near points. Nagoya Math. J. 109 (1988), 69-89. | DOI | MR | Zbl

[13] Mikulski, W. M.: The geometrical constructions lifting tensor fields of type $(0,2)$ on manifolds to the bundles of $A$-velocities. Nagoya Math. J. 140 (1995), 117-137. | DOI | MR | Zbl

[14] Morimoto, A.: Prolongations of connections to bundles of infinitely near points. J. Diff. Geom. 11 (1976), 479-498. | DOI | MR

[15] Weil, A.: Théorie des points proches sur les variétés différentielles. Colloques Internat. Centre Nat. Rech. Sci. 52 (1953), 111-117 French. | MR