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2008 Constant Mean Curvature Surfaces in Euclidean and Minkowski Three-Spaces
David Brander, Wayne Rossman, Nicholas Schmitt
J. Geom. Symmetry Phys. 12: 15-26 (2008). DOI: 10.7546/jgsp-12-2008-15-26


Spacelike constant mean curvature (CMC) surfaces in Minkowski 3-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 $\mathrm{SU}(2)$ with $\mathrm{SU}(1,1)$. 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.


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David Brander. Wayne Rossman. Nicholas Schmitt. "Constant Mean Curvature Surfaces in Euclidean and Minkowski Three-Spaces." J. Geom. Symmetry Phys. 12 15 - 26, 2008.


Published: 2008
First available in Project Euclid: 24 May 2017

zbMATH: 1159.53336
MathSciNet: MR2498778
Digital Object Identifier: 10.7546/jgsp-12-2008-15-26

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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