Backlund transformations of n-dimensional constant torsion curves

The Backlund transformation of two surfaces of R-3 with the same constant negative Gaussian curvature transforms an asymptotic line of one surface into an asymptotic line of the other. Since by Enneper the asymptotic lines of such a surface have constant torsion, it is natural to restrict the Backlund transformations to such curves. This idea was developed by ANNALISA CALINI and THOMAS IVEY in [2]. We shall prove the converse of their theorem and generalize the transformation for the n-dimensional case.