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

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

2009-07-09

arxiv.org/abs/0907.1479v2

Mathematics

Differential Geometry

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

Scientific paper

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

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