## Proceedings of the International Conference on Geometry, Integrability and Quantization

- Geom. Integrability & Quantization
- Proceedings of the Tenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2009), 133 - 142

### Constant Mean Curvature Surfaces in Euclidean and Minkowski Three-Spaces

David Brander, Wayne Rossman, and Nicholas Schmitt

#### Abstract

Spacelike constant mean curvature (CMC) surfaces in Minkowski three-space $\mathbb{L}^{3}$ have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group SU(2) with SU(1,1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop group, used to construct the surfaces, is not global. The construction is described here, with an emphasis on the difference from the Euclidean case.

#### Article information

**Dates**

First available in Project Euclid:
13 July 2015

**Permanent link to this document**

https://projecteuclid.org/
euclid.pgiq/1436793439

**Digital Object Identifier**

doi:10.7546/giq-10-2009-133-142

**Mathematical Reviews number (MathSciNet)**

MR2757829

**Zentralblatt MATH identifier**

1183.53005

#### Citation

Brander, David; Rossman, Wayne; Schmitt, Nicholas. Constant Mean Curvature Surfaces in Euclidean and Minkowski Three-Spaces. Proceedings of the Tenth International Conference on Geometry, Integrability and Quantization, 133--142, Avangard Prima, Sofia, Bulgaria, 2009. doi:10.7546/giq-10-2009-133-142. https://projecteuclid.org/euclid.pgiq/1436793439

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