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

Abstract

AbstractWe study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3using 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 Nil3with 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.