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Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces

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<mark>Journal publication date</mark>30/04/2021
<mark>Journal</mark>Discrete and Computational Geometry
Number of pages25
Pages (from-to)655–679
Publication StatusPublished
Early online date20/09/19
<mark>Original language</mark>English


We present a rigorous study of framework rigidity in general finite dimensional normed spaces from the perspective of Lie group actions on smooth manifolds. As an application, we prove an extension of Asimow and Roth’s 1978/1979 result establishing the equivalence of local, continuous and infinitesimal rigidity for regular bar-and-joint frameworks in a d-dimensional Euclidean space. Further, we obtain upper bounds for the dimension of the space of trivial motions for a framework and establish the flexibility of small frameworks in general non-Euclidean normed spaces.

Bibliographic note

The final publication is available at Springer via https://doi.org/10.1007/s00454-019-00135-5