×

On maximal surfaces in the \(n\)-dimensional Lorentz-Minkowski space. (English) Zbl 0732.53048

The authors prove several theorems of Bernstein type for complete space- like 2-dimensional surfaces in n-dimensional Minkowski space with zero mean curvature. For example they show that if all timelike normals to such a surface in \({\mathbb{E}}^ n_ 1\), \(n\geq 4\), omit a neighborhood of a fixed timelike direction, then the surface is a plane.
The authors erroneously refer to space-like zero mean curvature surfaces in \({\mathbb{E}}^ n_ 1\) as being maximal. This is only the case for \(n=3\).
Reviewer: B.Palmer (Berlin)

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
PDFBibTeX XMLCite
Full Text: DOI