The Euler like operators on touples of Lagrangians and functions on total spaces

Abstract

We  describe all Euler like operators $C$, i.e. natural operators transforming tuples $(\lambda,g)$ of Lagrangians $\lambda:J^sY\to\wedge^mT^*M$ on on a fibred manifold $Y\to M$ and functions $g:Y\to \mathbf{R}$  into Euler maps$(C(\lambda,g):J^{2s}Y\toV^*Y\otimes\wedge^mT^*M on $Y\to M$. The most important example of  such operators is the Euler operator $E$ (from the variational calculus) being the one in question depending only on Lagrangians. We describe all foruler like operators, too.