Straight ruled surfaces in the Heisenberg group
Differential Geometry
2014-01-30 v2
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.
Keywords
Cite
@article{arxiv.1212.5834,
title = {Straight ruled surfaces in the Heisenberg group},
author = {Ioannis D. Platis},
journal= {arXiv preprint arXiv:1212.5834},
year = {2014}
}
Comments
16 pages. Minor rearrangements, correction of typos and small additions have been made to the first version