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

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