The Bianchi-Darboux transform of L-isothermic surfaces
  We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutability theorem for iterated Bianchi-Darboux transforms. 
E. Musso, L. Nicolodi