Darboux transformations for twisted so(p,q) system and local isometric   immersion of space forms
  For the n-dimensional integrable system with a twisted so(p,q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are applied to the local isometric immersion of space forms with flat normal bundle and linearly independent curvature normals to give the explicit expression of the position vector. Some examples are given from the trivial solutions and standard imbedding T^n\to R^{2n}. 
Zixiang Zhou (Institute of Mathematics, Fudan University, Shanghai,   China)