## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 39, Number 1 (2010), 1-55.

### Complex surfaces of constant mean curvature fibered by minimal surfaces

Josef DORFMEISTER, Shimpei KOBAYASHI, and Franz PEDIT

#### 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.

#### Article information

**Source**

Hokkaido Math. J., Volume 39, Number 1 (2010), 1-55.

**Dates**

First available in Project Euclid: 19 May 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1274275018

**Digital Object Identifier**

doi:10.14492/hokmj/1274275018

**Mathematical Reviews number (MathSciNet)**

MR2649325

**Zentralblatt MATH identifier**

1202.53012

**Subjects**

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

**Keywords**

constant mean curvature minimal surfaces

#### Citation

DORFMEISTER, Josef; KOBAYASHI, Shimpei; PEDIT, Franz. Complex surfaces of constant mean curvature fibered by minimal surfaces. Hokkaido Math. J. 39 (2010), no. 1, 1--55. doi:10.14492/hokmj/1274275018. https://projecteuclid.org/euclid.hokmj/1274275018