Reducibility theorems for differentiable liftings in fiber bundles
Reduction theorem for general connections
We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.
Relations between constants of motion and conserved functions
We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.
Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold.
Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold
All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).
Remark on bilinear operations on tensor fields
This short note completes the results of [3] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [3] can be characterized in a completely algebraic way, even without any continuity assumption on the operations.
Remarques sur les problèmes comportant des inéquations différentielles globales
Remarques sur les systèmes différentiels
Ricci and Bianchi identities for -normal -linear connections on .
Riemannian structures on higher order frame bundles over Riemannian manifolds.