Enneper representation of minimal surfaces in the three-dimensional Lorentz-Minkowski space

Abstract

In this paper, we will give an Enneper-type representation for spacelike and timelike minimal surfaces in the Lorentz-Minkowski space $L^3$, using the complex and the paracomplex analysis (respectively). Then, we exhibit various examples of minimal surfaces in $L^3$ constructed via the Enneper representation formula, that it is equivalent to the Weierstrass representation obtained by Kobayashi (for spacelike immersions) and by Konderak (for the timelike ones).

17 pages, 9 figures