Laguerre geometry of surfaces with plane lines of curvature (Q1969671)

The authors continue their study of \(L\)-isothermic surfaces initiated in [the authors, New developments in differential geometry, Budapest 1996, 285-294 (1999; Zbl 0942.53006)]. Using moving frames, they find an integral formula for such surfaces and prove that an \(L\)-isothermic surface is \(L\)-congruent to either a cylindrical moulding surface, or a surface whose Gauss map coincides with that of Enneper's surface, for which they give explicit formulas. They also find formulas for \(L\)-isothermic \(L\)-minimal surfaces.