Hokkaido Mathematical Journal

DORFMEISTER Josef, KOBAYASHI Shimpei, PEDIT Franz,

Complex surfaces of constant mean curvature fibered by minimal surfaces.

Hokkaido Mathematical Journal, 39 (2010) pp.1-55

Fulltext

PDF

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(Primary)
MSC(Secondary)53A10(MSC2000)
Uncontrolled Keywordsconstant mean curvature; minimal surfaces;