Nonsymmetric metrics in nonlinear field theory

Algebraic and differential properties are considered of a nonsymmetric metrics introduced into field theory by Einstein and subsequently by Born and Infeld. It is shown that the nonsymmetric metrics is characterized by a pair of vector and a pair of covector fields connected by two identities. If these fields are zero, the nonsymmetric metrics is called harmonic one, an example is any metrics obeying the Born-Infeld equations. The theory of harmonic metrics may be considered as a direct generalization of the Born-Infeld theory