Sym-Bobenko formula for minimal surfaces in Heisenberg space
S\'ebastien Cartier (LAMA)
TL;DR
This paper introduces the Sym-Bobenko formula for minimal surfaces in Heisenberg space, enabling explicit surface construction and a generalized Weierstrass representation.
Contribution
It provides the first explicit immersion formula for minimal surfaces in Heisenberg space, expanding the tools for their analysis and construction.
Findings
Derived the Sym-Bobenko immersion formula for Heisenberg space
Established a generalized Weierstrass type representation
Constructed explicit examples of minimal surfaces
Abstract
We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces.
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