Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces

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 ($R^d$ 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.

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

References in corpus (2)

• Some notes on the equivalence of first-order rigidity in various geometries
• The number of equivalent realisations of a rigid graph