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

Abstract

In a previous paper we classified complete stationary surfaces (i.e. spacelike surfaces with zero mean curvature) in 4-dimensional Lorentz space $\mathbb{R}^4_1$ which are algebraic and with total Gaussian curvature $-\int K\mathrm{d}M=4\pi$. Here we go on with the study of such surfaces with $-\int K\mathrm{d}M=6\pi$. 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.