2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170676We 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.9 pages, minor corrections to terminologyDifferential GeometryDynamical Systems37K25; 53C42; 53B25text