  We give a loop group formulation for the problem of isometric immersions with
flat normal bundle of a simply connected pseudo-Riemannian manifold
$M_{c,r}^m$, of dimension $m$, constant sectional curvature $c \neq 0$, and
signature $r$, into the pseudo-Euclidean space $\real_s^{m+k}$, of signature
$s\geq r$. In fact these immersions are obtained canonically from the loop
group maps corresponding to isometric immersions of the same manifold into a
pseudo-Riemannian sphere or hyperbolic space $S_s^{m+k}$ or $H_s^{m+k}$, which
have previously been studied. A simple formula is given for obtaining these
immersions from those loop group maps.
