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Article Dans Une Revue Communications in Mathematics Année : 2023

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

Rory Biggs
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Résumé

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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hal-03894564 , version 1 (12-12-2022)
hal-03894564 , version 2 (03-01-2023)

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Rory Biggs, Odirile O.K.L. Ntshudisane. On the classification of sub-Riemannian structures on a 5D two-step nilpotent Lie group. Communications in Mathematics, In press, Volume 32 (2024), Issue 1 (1), pp.13-22. ⟨10.46298/cm.10550⟩. ⟨hal-03894564v2⟩
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