30 1. Classical Differential Geometry isothermic surfaces to curved flats (see Ferus-Pedit (1996)) was established in Burstall-Hertrich-Jeromin-Pedit-Pinkall (1997). A description of Bonnet pairs (pairs of isometric surfaces with the same mean curvature) in terms of isothermic surfaces was given in Kamberov-Pedit-Pinkall (1998). Isother- mic surfaces in multidimensional spaces were studied by Schief (2001) and Burstall (2006). A construction of Darboux transformations for isothermic surfaces using a quaternionic Riccati equation was suggested in Hertrich- Jeromin-Pedit (1997). A systematic presentation of the theory of isothermic surfaces and their transformations is given in Hertrich-Jeromin (2003). Section 1.8: Surfaces with constant mean curvature. The theory of surfaces with constant positive Gaussian curvature and their parallel surfaces (including surfaces with constant mean curvature) goes back to Bonnet and can be found, e.g., in Darboux (1914–27) and Bianchi (1923).
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