A role of exterior and evolutionary skew-symmetric differential forms in mathematical physics

Abstract:
A role of skew-symmetric differential forms in mathematical physics relates to the fact that they reflect properties of the conservation laws. The closed exterior forms are connected with conservation laws for physical fields. Evolutionary forms (the skew-symmetric differential forms defined on deforming manifolds) are also connected with conservation laws. However these conservation laws are for material media: the balance conservation laws for energy, linear momentum, angular momentum and mass. From the unclosed evolutionary forms under degenerate transformation (conditioned by symmetries)obtains the closed exterior form. It follows that physical fields are generated by the material media.