Jet geometrical extension of the KCC-invariants.
Given a Weil algebra and a smooth manifold , we prove that the set of kernels of regular -points of , , has a differentiable manifold structure and is a principal fiber bundle.
We review the approach to the calculus of variations using Ehresmann's theory of jets. We describe different types of jet manifold, different types of variational problem and different cohomological structures associated with such problems.