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

2019/03/03 by Dorfmeister, Josef F., Inoguchi, Jun-ichi, Kobayashi, Shimpei
#58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A10 #Secondary 53C42

paper · doi:10.48550/arxiv.1903.00795

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 discuss how to construct minimal surfaces in Nil₃ with non-trivial topology. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group Iso_∘(Nil₃) of Nil₃.

Related

• A loop group method for minimal surfaces in the three-dimensional Heisenberg group
• Ruled minimal surfaces in the three dimensional Heisenberg group
• The Gauss map of Minimal graphs in the Heisenberg group
• A duality for minimal surfaces in the Heisenberg group
• Timelike minimal surfaces in the three-dimensional Heisenberg group