Invariants for the Lagrangian equivalence problem

Let M be a connected smooth manifold, let Aut(p) be the group automorphisms of the bundle p:R×M→R, and let q:J1(R,M)×R→J1(R,M) be the canonical projection. Invariant functions on Jr(q) under the natural action of Aut(p) are discussed in relationship with the Lagrangian equivalence problem. The second-order invariants are determined geometrically as well as some other higher-order invariants for dim⁡M≥2.