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arXiv · 1908.01169

A car as parabolic geometry

C. Denson Hill·Paweł Nurowski
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Abstract

We show that a car, viewed as a nonholonomic system, provides an example of a flat parabolic geometry of type $({\bf SO}(2,3),P_{12})$, where $P_{12}$ is a Borel parabolic subgroup in ${\bf SO}(2,3)$. We discuss the relations of this geometry of a car with the geometry of circles in the plane (a low dimensional Lie sphere geometry), the geometry of 3-dimensional conformal Minkowski spacetime, the geometry of 3-rd order ODEs, projective contact geometry in three dimensions, and the corresponding twistor fibrations. We indicate how all these classical geometries can be interpreted in terms of the nonholonomic kinematics of a car.

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C. Denson Hill, Paweł Nurowski. 2019-08-03. A car as parabolic geometry. https://arxiv.org/abs/1908.01169

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