Jacobi vector fields and geodesic tubes in certain Kähler manifolds
We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.
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.