Isometric embedding of negatively curved complete surfaces in Lorentz-Minkowski space

Details Isometric embedding of negatively curved complete surfaces in Lorentz-Minkowski space Isometric embedding of negatively curved complete surfaces in Lorentz-Minkowski space

2011-09-20

arxiv.org/abs/1109.4211v2

Mathematics

Differential Geometry

18 pages

Scientific paper

Hilbert-Efimov theorem states that any complete surface with curvature
bounded above by a negative constant can not be isometrically imbedded in
$\mathbb{R}^3.$ We demonstrate that any simply-connected smooth complete
surface with curvature bounded above by a negative constant admits a smooth
isometric embedding into the Lorentz-Minkowski space $\mathbb{R}^{2,1}$.

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