A loop group method for minimal surfaces in the three-dimensional Heisenberg group
Differential Geometry
2015-01-26 v4
Abstract
We characterize constant mean curvature surfaces in the three-dimensional Heisenberg group by a family of flat connections on the trivial bundle over a simply connected domain in the complex plane. In particular for minimal surfaces, we give an immersion formula, the so-called Sym-formula, and a generalized Weierstrass type representation via the loop group method.
Cite
@article{arxiv.1210.7300,
title = {A loop group method for minimal surfaces in the three-dimensional Heisenberg group},
author = {Josef F. Dorfmeister and Jun-ichi Inoguchi and Shimpei Kobayashi},
journal= {arXiv preprint arXiv:1210.7300},
year = {2015}
}
Comments
40 pages, v2: The argument for branch points has been fixed and the references have been updated. v3: The argument for canonical examples has been fixed and the classification for homogeneous surfaces has been added v4: Some typos are fixed and Remark 5.4 (3) is added