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arXiv · 2405.16898

The CR geometry of the three-segment snake

Tymon Frelik
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Abstract

We study the geometry associated with the kinematics of a planar robot known as the "three-segment snake," whose velocity distribution belongs to a class of (2,3,5) distributions. We discover that, under certain assumptions on its construction parameters, the snake may be endowed with a CR structure of CR dimension 1 and real codimension 3. We solve the associated Cartan equivalence problem and find the invariants of the snake's CR structure.

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Tymon Frelik. 2024-05-27. The CR geometry of the three-segment snake. https://arxiv.org/abs/2405.16898

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