The CR geometry of the three-segment snake
Differential Geometry
2024-05-28 v1
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.
Cite
@article{arxiv.2405.16898,
title = {The CR geometry of the three-segment snake},
author = {Tymon Frelik},
journal= {arXiv preprint arXiv:2405.16898},
year = {2024}
}
Comments
6 pages, 1 figure