  Identical relations occur in various branches of mathematics and mathematical
physics. The Cauchy-Riemann relations, characteristical and canonical
relations, the Bianchi identities and others are examples of identical
relations. It can be shown that all these relations express either the
conditions of closure of exterior (skew-symmetric) differential forms and
corresponding dual forms or the properties of closed exterior forms. Since the
closed differential forms are invariant under all transformations, which
conserve the differential (these are gauge transformations: unitary, canonical,
gradient and others), from this it follows that identical relations are a
mathematical representation of relevant invariant and covariant objects.
  The theory of exterior differential forms cannot answer the question of how
do invariant objects appear and what does these objects generate?
  The answer to this question can be obtained using the skew-symmetric
differential forms, which possess the evolutionary properties. The mathematical
apparatus of such evolutionary forms contains nonidentical relations, from
which the identical relations corresponding to invariant objects are obtained
with the help of degenerate transformations. Due to such potentialities, the
mathematical apparatus of skew-symmetrical differential forms enables one to
describe discrete transitions, evolutionary processes and generation of various
structures.
