Bonnet Surfaces and Isothermic Surfaces

By the study of the relations between Bonnet surfaces and isothermic surfaces, we obtain classification results of Bonnet surfaces in 3-dimensional space form R3(c) and of the spacelike Bonnet surfaces in indefinite space form R1 3(c), which generalize the results in Bobenko’s [1] and Peng-Lu’s [11]. It is remarkable that there exist always Bonnet surfaces which are not Weingarten surfaces, if the ambient space is not R3(c) for c ≥ 0.