On the classification of sub-Riemannian structures on a 5D two-step nilpotent Lie group

We classify the left-invariant sub-Riemannian structures on the unique five-dimensional simply connected two-step nilpotent Lie group with two-dimensional commutator subgroup; this 5D group is the first twostep nilpotent Lie group beyond the three-and five-dimensional Heisenberg groups. Alongside, w...

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Veröffentlicht in:Communications in Mathematics 2023-01, Vol.32 (2024), Issue 1 (1), p.13-22
Hauptverfasser: Biggs, Rory, Ntshudisane, Odirile
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container_volume 32 (2024), Issue 1
creator Biggs, Rory
Ntshudisane, Odirile
description We classify the left-invariant sub-Riemannian structures on the unique five-dimensional simply connected two-step nilpotent Lie group with two-dimensional commutator subgroup; this 5D group is the first twostep nilpotent Lie group beyond the three-and five-dimensional Heisenberg groups. Alongside, we also present a classification, up to automorphism, of the subspaces of the associated Lie algebra (together with a complete set of invariants).
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title On the classification of sub-Riemannian structures on a 5D two-step nilpotent Lie group
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