  We impose in the nonsymmetric gravitational theory, by means of Lagrange
multiplier fields in the action, a set of covariant constraints on the
antisymmetric tensor field. The canonical Hamiltonian constraints in the weak
field approximation for the antisymmetric sector yield a Hamiltonian energy
bounded from below. An analysis of the Cauchy evolution, in terms of an
expansion of the antisymmetric sector about a symmetric Einstein background,
shows that arbitrarily small antisymmetric Cauchy data can lead to smooth
evolution.
