Ruled minimal surfaces in the three dimensional Heisenberg group

Details Ruled minimal surfaces in the three dimensional Heisenberg group Ruled minimal surfaces in the three dimensional Heisenberg group

2009-06-06

arxiv.org/abs/0906.1246v1

Mathematics

Differential Geometry

18 pages

Scientific paper

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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