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

Bing-Long Chen and Le Yin

Vol. 276 (2015), No. 2, 347–367

DOI: 10.2140/pjm.2015.276.347

Abstract

The Hilbert–Efimov theorem states that any complete surface with curvature bounded above by a negative constant cannot be isometrically embedded in ${ℝ}^{\mathfrak{3}}$. 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 ${ℝ}^{\mathfrak{2},\mathfrak{1}}$.

Keywords

isometric embedding, Hilbert–Efimov theorem, Lorentz–Minkowski space

Mathematical Subject Classification 2010

Primary: 53C21

Secondary: 35J96

Milestones

Received: 28 August 2014

Accepted: 5 January 2015

Published: 15 July 2015