Complex surfaces of constant mean curvature fibered by minimal surfaces

Authors

J Dorfmeister
S Kobayashi
F Pedit, University of Massachusetts - AmherstFollow

Publication Date

2010

Journal or Book Title

HOKKAIDO MATHEMATICAL JOURNAL

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.

Comments

The published version is located at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.hokmj/1274275018

Pages

1-55

Volume

39

Issue

1

Recommended Citation

Dorfmeister, J; Kobayashi, S; and Pedit, F, "Complex surfaces of constant mean curvature fibered by minimal surfaces" (2010). HOKKAIDO MATHEMATICAL JOURNAL. 754.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/754