Ribaucour transformations for isometric immersions of pseudo-Riemannian space forms

In this paper, we give the explicit construction for isometric immersions of pseudo-Riemannian space forms via loop group actions. As a consequence, we obtain a Ribaucour transformation and its permutability theorem for isometric immersions of pseudo-Riemannian space forms, which is a generalization of the permutability theorem for surfaces in R3R3, and a family of new isometric immersions of the pseudo-Riemannian space forms from a given one via a purely algebraic algorithm.