ABSTRACT
In 1879, Luigi Bianchi gave for the first time in his thesis a method for deriving from one surface of constant negative Gaussian curvature an infinite number of other surfaces with the same curvature. His work created great interest and was followed by papers by Darboux, Lie, and Backlund. In [Bck], Backlund gave a more general construction that led to the Backlund transform. In spite of the fact that the paper [Bck] dealt exclusively with surfaces of constant negative curvature, the notion of Backlund transform has come to have enormous importance in soliton theory (see for example [Lamb2, Remo]).
