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Complex surfaces of constant mean curvature fibered by minimal surfaces. (English) Zbl 1202.53012
Authors’ abstract: We define complex constant mean curvature immersions in complex three space using a natural extension of constant mean curvature immersions in Euclidean three space via loop group techniques. We then discuss the fundamental properties of these complex constant mean curvature immersions. In particular, we prove that these immersions are doubly ruled by holomorphic null curves. We present a construction of minimal immersions from constant mean curvature immersions in Euclidean three space via the associated complex constant mean curvature immersions.

##### MSC:
 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
##### Keywords:
constant mean curvature; minimal surfaces
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