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Affine rigidity and conics at infinity

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dc.contributor.authorConnelly, Robert
dc.contributor.authorGortler, Steven J.
dc.contributor.authorTheran, Louis
dc.date.accessioned2018-02-27T00:32:39Z
dc.date.available2018-02-27T00:32:39Z
dc.date.issued2018-07
dc.identifier.citationConnelly , R , Gortler , S J & Theran , L 2018 , ' Affine rigidity and conics at infinity ' , International Mathematics Research Notices , vol. 2018 , no. 13 , pp. 4084-4102 . https://doi.org/10.1093/imrn/rnx014en
dc.identifier.issn1073-7928
dc.identifier.otherPURE: 248917121
dc.identifier.otherPURE UUID: d4068065-7959-4874-a875-777e5622fcef
dc.identifier.otherScopus: 85057832522
dc.identifier.otherWOS: 000441676600005
dc.identifier.otherORCID: /0000-0001-5282-4800/work/73701813
dc.identifier.urihttp://hdl.handle.net/10023/12792
dc.descriptionRC is partially supported by NSF grant DMS-1564493. SJG is partially supported by NSF grant DMS-1564473.en
dc.description.abstractWe prove that if a framework of a graph is neighborhood affine rigid in d-dimensions (or has the stronger property of having an equilibrium stress matrix of rank n — d — 1) then it has an affine flex (an affine, but non Euclidean, transform of space that preserves all of the edge lengths) if and only if the framework is ruled on a single quadric. This strengthens and also simplifies a related result by Alfakih. It also allows us to prove that the property of super stability is invariant with respect to projective transforms and also to the coning and slicing operations. Finally this allows us to unify some previous results on the Strong Arnold Property of matrices.
dc.format.extent19
dc.language.isoeng
dc.relation.ispartofInternational Mathematics Research Noticesen
dc.rights© 2017, the Author(s). This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at imrn.oxfordjournals.org / https://doi.org/10.1093/imrn/rnx014en
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subject.lccQAen
dc.titleAffine rigidity and conics at infinityen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1093/imrn/rnx014
dc.description.statusPeer revieweden
dc.date.embargoedUntil2018-02-26
dc.identifier.urlhttps://arxiv.org/abs/1605.07911en


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