Implicit equations of the Henneberg-type minimal surface in the four-dimensional Euclidean space (Q2337240)

Summary: Considering the Weierstrass data as \((\psi, f, g) = (2, 1 - z^{-m}, z^n)\), we introduce a two-parameter family of Henneberg-type minimal surface that we call \(\mathfrak{H}_{m, n}\) for positive integers \((m, n)\) by using the Weierstrass representation in the four-dimensional Euclidean space \(\mathbb{E}^4\). We define \(\mathfrak{H}_{m, n}\) in \((r, \theta)\) coordinates for positive integers \((m, n)\) with \(m \neq 1,n\neq -1, -m+n \neq -1\), and also in \((u, v)\) coordinates, and then we obtain implicit algebraic equations of the Henneberg-type minimal surface of values \((4, 2)\).