Real forms of complex surfaces of constant mean curvature

@inproceedings{Kobayashi2011RealFO,
  title={Real forms of complex surfaces of constant mean curvature},
  author={Shimpei Kobayashi},
  year={2011}
}
It is known that complex constant mean curvature ({\sc CMC} for short) immersions in $\mathbb C^3$ are natural complexifications of {\sc CMC}-immersions in $\mathbb R^3$. In this paper, conversely we consider {\it real form surfaces} of a complex {\sc CMC}-immersion, which are defined from real forms of the twisted $\mathfrak{sl}(2, \mathbb C)$ loop algebra $\Lambda \mathfrak{sl}(2, \mathbb C)_\sigma$, and classify all such surfaces according to the classification of real forms of $\Lambda… CONTINUE READING

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