The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Abstract

We consider the Enneper family of real maximal surfaces via Weierstrass data (1,zeta(m)) for zeta & ISIN;C, m & ISIN;Z & GE;1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E-2,E-1. Moreover, we propose that the family has degree (2m+1)(2) (resp., class 2m(2m+1)) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).