We present a Möbius invariant construction of the Darboux transformation for isothermic surfaces by the method of moving frames and use it to give a complete classification of the Darboux transforms of Dupin surfaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-9, author = {Emilio Musso and Lorenzo Nicolodi}, title = {Darboux transforms of Dupin surfaces}, journal = {Banach Center Publications}, volume = {58}, year = {2002}, pages = {135-154}, zbl = {1029.53022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-9} }
Emilio Musso; Lorenzo Nicolodi. Darboux transforms of Dupin surfaces. Banach Center Publications, Tome 58 (2002) pp. 135-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-9/