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Keywords:
natural operator; Weil bundle
natural operator; Weil bundle
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.
References:
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