On lifting of 2-vector fields to \(r\)-jet prolongation of the tangent bundle

Jan Kurek, Włodzimierz Mikulski

Abstract


If \(m \geq 3\) and \(r \geq 1\), we prove that any natural linear operator \(A\) lifting 2-vector fields \(\Lambda \in \Gamma (\bigwedge^2 TM)\) (i.e., skew-symmetric tensor fields of type (2,0)) on \(m\)-dimensional manifolds \(M\) into 2-vector fields \(A(\Lambda)\) on \(r\)-jet prolongation \(J^rTM\) of the tangent bundle \(TM\) of \(M\) is the zero one.

Keywords


Natural operator; 2-vector field; r-jet prolongation

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References


Debecki, J., Linear natural lifting p-vectors to tensors of type (q,0) on Weil bundles, Czechoslovak Math. J. 66(141) (2) (2016), 511–525.

Kolar, I, Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.

Mikulski, W. M., The linear natural operators lifting 2-vector fields to some Weil bundles, Note di Math. 19(2) (1999), 213–217.




DOI: http://dx.doi.org/10.17951/a.2021.75.1.61-67
Date of publication: 2021-07-24 12:07:02
Date of submission: 2021-07-21 22:18:38


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