On G2 and sub-Riemannian model spaces of step and rank three
Peer reviewed, Journal article
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Date
2021Metadata
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- Institutt for matematiske fag [2530]
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Abstract
We give the complete classification of all sub-Riemannian model spaces with both step and rank three. Model spaces in this context refer to spaces where any infinitesimal isometry between horizontal tangent spaces can be integrated to a full isometry. They will be divided into three families based on their nilpotentization. Each family will depend on a different number of parameters, making the result crucially different from the known case of step two model spaces. In particular, there are no nontrivial sub-Riemannian model spaces of step and rank three with free nilpotentization. We also realize both the compact real form gc2 and the split real form gs2 of the exceptional Lie algebra g2 as isometry algebras of different model spaces.