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arXiv · 2108.04599

Local equivalence of some maximally symmetric $(2,3,5)$-distributions

Matthew Randall
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Abstract

Using a complex parametrisation of $su(2)$, we show a change of coordinates that maps the maximally symmetric rolling $(2,3,5)$-distribution to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric rolling model and the flat Cartan or Hilbert-Cartan distribution. For the maximally symmetric rolling distribution, we write down the vector fields that bracket-generate to give the split real form of the Lie algebra of $\frak{g}_2$, with two of the vector fields in the bracket-generating set given by the span of the rolling distribution.

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Matthew Randall. 2021-08-10. Local equivalence of some maximally symmetric $(2,3,5)$-distributions. https://arxiv.org/abs/2108.04599

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