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arXiv · 1902.09210

The global rigidity of a framework is not an affine-invariant property

Victor Alexandrov
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Abstract

It is well-known that the property of a bar-and-joint framework `to be infinitesimally rigid' is invariant under projective transformations of Eucliean $d$-space for every $d\geqslant 2$. It is less known that the property of a bar-and-joint framework `to be globally rigid' is not invariant even under affine transformations of the Euclidean plane. In this note, we prove of the latter statement for Euclidean $d$-space for every $d\geqslant 2$.

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Victor Alexandrov. 2019-02-25. The global rigidity of a framework is not an affine-invariant property. https://arxiv.org/abs/1902.09210

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