  We suppose that our Universe is closed manifold in real embedding higher
dimensional space. This model well describes expanding character of Universe
where each point becomes more far from any other point with time. We have
derived Klein-Gordon equation using the symmetry of Universe expansion.
Comparing it with squared Dirac-Fock-Ivanenko equation we have derived
expression for gravitationally induced chiral current. Starting from the
expression for gravitationally induced chiral current obtained on the basis of
brane symmetry we have shown that being placed into the Einstein's
gravitational field, chiral current yields inertial gravitational field. This
inertial gravitational field transforms into the vortex gravitational field and
then back to the inertial gravitational field thus ensuring the propagation of
such kind of gravitational excitation as constitutional part of gravitational
wave. In the case of weak gravitation, these symmetry considerations and our
consequent equations lead directly to harmonic gauge conditions that are
necessary for supplementing Einstein equations.
