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

Alma L. Albujer; Luis J. Alias

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arXiv · 0907.1479

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

Alma L. Albujer·Luis J. Alias

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Abstract

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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BibTeX RIS

Alma L. Albujer, Luis J. Alias. 2009-08-25. A Hilbert-type theorem for spacelike surfaces with constant Gaussian curvature in $\mathbb{H}^2\times\mathbb{R}_1$. https://arxiv.org/abs/0907.1479

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