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Ruled minimal surfaces in the three dimensional Heisenberg group

Differential Geometry 2009-06-09 v1

Abstract

It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three dimensional Heisenberg group whose mean curvature is zero with respect to both of the standard Riemannian metric and the standard Lorentzian metric.

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Cite

@article{arxiv.0906.1246,
  title  = {Ruled minimal surfaces in the three dimensional Heisenberg group},
  author = {Young Wook Kim and Sung-Eun Koh and Hyung Yong Lee and Heayong Shin and Seong-Deog Yang},
  journal= {arXiv preprint arXiv:0906.1246},
  year   = {2009}
}

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18 pages