2-forms induced by Lagrangians on Weil bundles (Q2777569)

For a differentiable manifold \(M\) let \(A\) and \(B\) be Weil algebras. In a natural way one can define an equivalence relation for maps \(f:\mathbb R^k \to M\) to ensure that the equivalence classes \(j^A f\), called \(A\)-velocities, fill in a Weil bundle \(T^A M\) over \(M\). Let \(Q: B \to A\) be an algebra epimorphism and let \(Q_M: T^B M \to T^A M\) be the canonical extension of \(Q\) from the bundle of \(B\)-velocities to the bundle of \(A\)-velocities over a manifold \(M\) defined by \textit{A.~Morimoto} [J. Differ. Geom. 11, 479-498 (1976; Zbl 0358.53013)]. In [Geom. Dedicata 67, No.1, 83-106 (1997; Zbl 0890.58001)] the author studied and classified all natural operators transforming either real-valued functions or 1-forms on \(T^A M\) into real-valued functions or 1-forms on \(T^B M\) over \(M\) of finite order with respect to \(Q\). NEWLINENEWLINENEWLINEIn this paper, the author classify all natural operators transforming functions \(T^A M\to \mathbb R\) into 2-forms on \(T^B M\) over \(M\) of finite order with respect to \(Q\).