Complete stationary surfaces in R^4_1 with total Gaussian curvature 6\pi

In a previous paper we classified complete stationary surfaces (i.e. spacelike surfaces with zero mean curvature) in 4-dimensional Lorentz space ${\mathbb{R}}_1^4$ which are algebraic and with total Gaussian curvature $-\int K$\mathrm{d}$M=4\pi$\mathrm{.}Herewegoonwiththestudyofsuchsurfaceswith$-\int K$\mathrm{d}$M=6\pi$. It is shown in this paper that the topological type of such a surface must be a M"obius strip. On the other hand, new examples with a single good singular end are shown to exist.