Abresch, Uwe; Rosenberg, Harold Generalized Hopf differentials. (English) Zbl 1118.53036 Mat. Contemp. 28, 1-28 (2005). The authors extend the idea of the Hopf differential in the study of constant mean curvature surfaces of the sphere to surfaces in product spaces like \(S^2\times \mathbb R\) and \(H^2\times \mathbb R\) by restoring holomorphicity by a geometric correction term. More generally this construction can be applied to surfaces in homogeneous 3-manifolds that fibre over a surface with totally geodesic fibres, and this is the appropriate class for which the developed method will work. Reviewer: Dirk Ferus (Berlin) Cited in 7 ReviewsCited in 58 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C20 Global Riemannian geometry, including pinching 53C30 Differential geometry of homogeneous manifolds Keywords:constant mean curvature; holomorphic differential; product spaces PDFBibTeX XMLCite \textit{U. Abresch} and \textit{H. Rosenberg}, Mat. Contemp. 28, 1--28 (2005; Zbl 1118.53036)