THE SPECTRAL INTERPRETATION OF N-SPACES OF CONSTANT NEGATIVE CURVATURE IMMERSED IN R2N-1

We show that immersions of n-dimensional space forms in R2n-1 (i.e., i mmersions of constant sectional curvature) can be explicitly expressed (by the Sym-Tafel formula) in terms of the wave function of the corre sponding spectral problem. Moreover, we suggest a method to discretize the immersions and the associated nonlinear system (a generalization of the sine-Gordon equation). (C) 1997 Elsevier Science B.V.