Prescribed Schouten Tensor in Locally Conformally Flat Manifolds

We consider the pseudo-Euclidean space (R-n, g), with n >= 3 and g(ij) = delta(ij epsilon i), where epsilon(i) = +/- 1, with at least one positive ei and non-diagonal symmetric tensors T = Sigma(i, j) f(ij)(x)dx(i) circle times dx(j). Assuming that the solutions are invariant by the action of a translation (n-1)- dimensional group, we find the necessary and sufficient conditions for the existence of a metric (g) over bar conformal to g, such that the Schouten tensor (g) over bar, is equal to T. From the obtained results, we show that for certain functions h, defined in R-n, there exist complete metrics (g) over bar, conformal to the Euclidean metric g, whose curvature sigma(2)((g) over bar) = h.