Hokkaido Mathematical Journal

Complex surfaces of constant mean curvature fibered by minimal surfaces

Josef DORFMEISTER, Shimpei KOBAYASHI, and Franz PEDIT

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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


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