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

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 $-\int K\mathrm{d}M=4π$. Here we go on with the study of such surfaces with $-\int K\mathrm{d}M=6π$. It is shown in this paper that the topological type of such a surface must be a Möbius strip. On the other hand, new examples with a single good singular end are shown to exist.

16 pages. The original proof of Lemma 4.1 is not correct because the Laurent series I used converges only locally; instead my new proof uses partial fraction decomposition which is always valid on the whole extended complex plane. Several math typos are corrected. A reference is removed. Accepted for publication on Differential Geometry and its Applications