(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

Abstract

We introduce the real minimal surfaces family by using the Weierstrass data (ζ−m,ζm) for ζ∈C, m∈Z≥2, then compute the irreducible algebraic surfaces of the surfaces family in three-dimensional Euclidean space E3. In addition, we propose that family has a degree number (resp., class number) 2m(m+1) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).