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

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

#### 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

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