English

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}
}