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

Xiang Ma

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

Differential Geometry 2014-02-17 v2

Authors: Xiang Ma

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.

Keywords

stationary surfaces Lorentz space total Gaussian curvature spacelike surfaces zero mean curvature M\"obius strip singular end

Cite

@article{arxiv.1211.0657,
  title  = {Complete stationary surfaces in R^4_1 with total Gaussian curvature 6\pi},
  author = {Xiang Ma},
  journal= {arXiv preprint arXiv:1211.0657},
  year   = {2014}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

Related papers