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 ( 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