The rigidity of periodic frameworks as graphs on a fixed torus

2012/02/29 by Elissa Ross, Ross, Elissa · 2 citations
Mathematics · #52C25 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52C25

paper · pdf · doi:10.48550/arxiv.1202.6652

42 pages, 9 figures

arxiv created 2012/02/29 · arxiv updated 2012/03/01

Abstract

We define periodic frameworks as graphs on the torus, using the language of gain graphs. We present some fundamental definitions and results about the infinitesimal rigidity of graphs on a torus of fixed size and shape, and find necessary conditions for the generic rigidity of pe- riodic frameworks on a d-dimensional fixed torus.

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• Uniquely realizable crystalline structures
• Non-Euclidean Crystallographic Rigidity

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