Generalized forms, vector fields and superspace

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.