Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds
Differential Geometry
2018-02-15 v2
Abstract
We prove that any metric of non-positive curvature in the sense of Alexandrov on a compact surface can be isometrically embedded as a convex spacelike Cauchy surface in a flat spacetime of dimension (2+1). The proof follows from polyhedral approximation.
Keywords
Cite
@article{arxiv.1703.07253,
title = {Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds},
author = {François Fillastre and Dmitriy Slutskiy},
journal= {arXiv preprint arXiv:1703.07253},
year = {2018}
}