Straight ruled surfaces in the Heisenberg group

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.

16 pages. Minor rearrangements, correction of typos and small additions have been made to the first version

References in corpus (4)

• Minimal surfaces in the Heisenberg group
• The Bernstein Problem in the Heisenberg Group
• Minimal surfaces in pseudohermitian geometry
• Stable complete embedded minimal surfaces in ${\mathbb{H}}^1$ with empty characteristic locus are vertical planes

Cited by in corpus (1)

• Modulus of surface families and the radial stretch in the Heisenberg group