In Ivey and Landsberg's book *Cartan for Beginners*, the end paragraph of example 5.8.2 claims that linear Weingarten surfaces can be constructed by a space curve. They cite an older book from 1945 that is in French (*Les Systemes Exterieurs et leurs Applications Geometriques*) which explicitly carries out this construction. 


I don't know French and I can't seem to find an English translation. Does anyone know of an English version? If not, does anyone know this construction and could give a brief outline of how it works? 



Construction of a linear Weingarten surface from a space curve
You'll find a discussion of the analysis of linear Weingarten surfaces via exterior differential systems in [these lecture notes of mine](https://services.math.duke.edu/~bryant/MSRI_Lectures.pdf). Particularly look at Section 5.1, where it is discussed at length. If you've already read Ivey and Landsberg, this should be fairly accessible.


I should say that this is not original work. The exposition is based on the treatment in Élie Cartan's book *Les systèmes différentiels extérieurs et leurs applications géométriques*. It's not exactly a translation, because Cartan did not use the same kind of 'set theory' language that we do now, but it's the same in spirit.


