Minimal cylinders in the three-dimensional Heisenberg group
Abstract
We study minimal cylinders in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method. We characterize all non-vertical minimal cylinders in terms of pairs of two closed plane curves which have the same signed area. Moreover, as a byproduct of the construction, spacelike CMC cylinders can also be obtained.
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