40 46 v 1 2 0 A pr 2 00 4 PHYSICAL STRUCTURES . FORMING PHYSICAL FIELDS AND MANIFOLDS ( Properties of skew - symmetric differential forms )

It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential forms. This apparatus discloses the controlling role of the conservation laws in evolutionary processes, which proceed in material media and lead to origination of physical structures and forming physical fields and manifolds. The closure conditions of the inexact exterior differential form and dual form (the equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. In this section it will be shown that as the physical structures, which form physical fields, it serve those, which in their properties are such differential-geometrical structures. The properties of such differential-geometrical structures, and correspondingly physical structures, are based on the properties of closed exterior differential forms. Below the properties of closed exterior differential forms are briefly described. (In more detail about skew-symmetric differential forms one can read in [1,2]. With the theory of exterior differential forms one can become familiar from the works [3-7]). The exterior differential form of degree p (p-form on the differentiable manifold) is called a closed one if its differential equals zero: dθ p = 0 (1) From condition (1) one can see that the closed form is a conservative quantity. This means that such a form can correspond to the conservation law, namely, to some conservative physical quantity. If the form is closed on pseudostructure only (i.e. it is the closed inexact differential form), the closure condition is written as d π θ p = 0 (2)