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arXiv · 1212.5834

Straight ruled surfaces in the Heisenberg group

Ioannis D. Platis
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Abstract

We generalise a result of Garofalo and Pauls: a horizontally minimal smooth surface embedded in the Heisenberg group is locally a (straight) ruled surface, i.e. it consists of straight lines tangent to a horizontal vector field along a smooth curve. We show additionally that any horizontally minimal surface is locally contactomorphic to the complex plane.

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Ioannis D. Platis. 2013-01-03. Straight ruled surfaces in the Heisenberg group. https://doi.org/10.1007/s00022-013-0199-6

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