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

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

Differential Geometry 2009-08-25 v2

Authors: Alma L. Albujer , Luis J. Alias

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 $K>-1$ .

Keywords

spacelike surfaces constant Gaussian curvature Lorentzian product Hilbert-type theorem $\mathbb{H}^2\times\mathbb{R}_1$

Cite

@article{arxiv.0907.1479,
  title  = {A Hilbert-type theorem for spacelike surfaces with constant Gaussian curvature in $\mathbb{H}^2\times\mathbb{R}_1$},
  author = {Alma L. Albujer and Luis J. Alias},
  journal= {arXiv preprint arXiv:0907.1479},
  year   = {2009}
}

Comments

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

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