Abstract
The generalized sine-Gordon system is an integrable system implicitly describing submanifolds of negative constant curvature in Euclidean spaces. To obtain the associated spectral problem we consider immersions of these submanifolds in spheres. The spectral parameter turns out to be related to the radius of the spheres. We also derive the so-called Sym-Tafel formula which yields the radius vector of negative constant curvature submanifolds in Euclidean spaces.