Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group

Abstract

We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will present a general scheme for how to construct minimal surfaces in Nil3 with non-trivial geometry. Special emphasis will be put on equivariant minimal surfaces. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group Iso◦(Nil3) of Nil3.

Keywords

• minimal surfaces
• heisenberg group
• symmetries
• generalized weierstrass type representation
• primary 53a10, 58e20
• secondary 53c42