A Hilbert-type theorem for spacelike surfaces with constant Gaussian curvature in ${\mathbb{H}}^2\times {\mathbb{R}}_1$

Abstract

There are examples of complete spacelike surfaces in the Lorentzian product ${\mathbb{H}}^2\times {\mathbb{R}}_1$ with constant Gaussian curvature $K\le -1$. In this paper, we show that there exists no complete spacelike surface in ${\mathbb{H}}^2\times {\mathbb{R}}_1$ with constant Gaussian curvature $K>-1$.

First version. May 2009. Final version (August 2009). To appear in the Bulletin of the Brazilian Mathematical Society

References in corpus (2)

• Calabi-Bernstein results for maximal surfaces in Lorentzian product spaces
• On the scalar curvature of hypersurfaces in spaces with a Killing field