DARBOUX TRANSFORMATIONS FOR THE TWISTED SO(P,Q) SYSTEM AND LOCAL ISOMETRIC IMMERSION OF SPACE-FORMS

For the n-dimensional integrable system with a twisted s o(p, q) reduc tion, Darboux transformations given by Darboux matrices of degree two are constructed explicitly. These Darboux transformations are applied to the local isometric immersion of space forms with flat normal bundl e and linearly-independent curvature normals to give the explicit expr ession of the position vector. Some examples are given from the trivia l solutions and standard imbedding T-n --> R-2n.