Remarks on the Darboux transform of isothermic surfaces. (English) Zbl 0892.53003
Using quaternionic calculus [see also the supplementary paper by U. Hertrich-Jeromin, ibid., 335-350 (1997; Zbl 0892.53004), reviewed below], the authors study Darboux and Christoffel transforms of isothermic surfaces in Euclidean space and derive a Riccati equation that characterizes all Darboux transforms of a given isothermic surface.
Reviewer: G.Thorbergsson (Köln)
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
