GENERALIZATION OF THE MONGE-AMPERE EQUATI ON TO COMPACT HERMITIAN-MANIFOLDS

Let (X, g) be a compact hermitian manifold. If phi belongs to C-2 (X), let us consider the changes of hermitian metric defined by g(1) (phi) = -phi g + i partial derivative partial derivative phi and g(2)(+/-)( phi) = g + i partial derivative partial derivative phi +/- del phi x d el phi. We solve equations of the form [det g(i) (phi)][det(g)](-1) = F (x, del phi; phi), where F is an element of C-infinity (TX x R) is a n everywhere strictly positive function satisfying some growth assumpt ions.