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