W.M. Mikulski
Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle

Comment.Math.Univ.Carolinae 43,3 (2002) 565-573.

Abstract:For natural numbers $r$ and $n\geq 2$ all natural operators $T_{\vert \Cal M f_n}\rightsquigarrow T^* (J^rT^{*})$ transforming vector fields from $n$-manifolds $M$ into $1$-forms on $J^r T^{*}M=\{j^r_x (\omega )\mid \omega \in \Omega ^1(M), x\in M\}$ are classified. A similar problem with fibered manifolds instead of manifolds is discussed.

Keywords: natural bundle, natural operator
AMS Subject Classification: 58A20