Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces

  • Steven J. GortlerEmail author
  • Dylan P. Thurston
Part of the Fields Institute Communications book series (FIC, volume 70)


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 (\(\mathbb{R}^{d}\) 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.


Metric geometry 

Subject Classifications

52C25 51M10 05C62 



We would like to thank Robert Connelly, Bill Jackson, John Owen, Louis Theran, and for helpful conversations and suggestions. We would especially like to thank Walter Whiteley for sharing with us his explanation of the Pogorelov map.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer SciencesHavard School of Engineering and Applied SciencesCambridgeUSA
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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