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arXiv · 0906.1246

Ruled minimal surfaces in the three dimensional Heisenberg group

Young Wook Kim·Sung-Eun Koh·Hyung Yong Lee·Heayong Shin·Seong-Deog Yang
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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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Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee, Heayong Shin, Seong-Deog Yang. 2009-06-06. Ruled minimal surfaces in the three dimensional Heisenberg group. https://arxiv.org/abs/0906.1246

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