English

Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces

Metric Geometry 2017-08-29 v4

Abstract

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space (RdR^d with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rigidity is always a generic property of a graph in complex space, and give a sufficient condition for it to be a generic property in a pseudo-Euclidean space. Extensions to hyperbolic space are also discussed.

Keywords

Cite

@article{arxiv.1212.6685,
  title  = {Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces},
  author = {Steven J. Gortler and Dylan P. Thurston},
  journal= {arXiv preprint arXiv:1212.6685},
  year   = {2017}
}

Comments

Changed numbering to agree with published version. One small correction in Lemma 3

R2 v1 2026-06-21T23:01:38.745Z