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

2021/08/10 by Matthew Randall, Randall, Matthew · 1 citation
Decision Sciences · Mathematics · #58A15 #58A17 #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Approximation and Integration #Probability and Risk Models #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2108.04599

openalex publication_date 2021/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \frakg₂, with two of the vector fields in the bracket-generating set given by the span of the rolling distribution.

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