Faculty of Computational Mathematics and Cybernetics,

Moscow State University,

2nd Educational Building,

Vorobjovy Gory,

Moscow 119899,

RUSSIA

E-mail: ptr@cs.msu.su

**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.