  Vector fields with components which are generalized zero-forms are
constructed. Inner products with generalized forms, Lie derivatives and Lie
brackets are computed. The results are shown to generalize previously reported
results for generalized vector fields. Hamiltonian vector fields are discussed.
Generalized affine connections and metrics are defined and the fundamental
theorem of metric differential geometry is extended. The global structure of
the exterior derivative of generalized forms is investigated.
