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

Abstract

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 ${\mathbb{R}}^{2,1}$.

18 pages

Cited by in corpus (1)

• Rigidity of isometric immersions into the light cone