Rory Biggs ; Odirile Ntshudisane - On the classification of sub-Riemannian structures on a 5D two-step nilpotent Lie group

cm:10550 - Communications in Mathematics, January 16, 2023, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.10550
On the classification of sub-Riemannian structures on a 5D two-step nilpotent Lie groupArticle

Authors: Rory Biggs 1; Odirile Ntshudisane 1

  • 1 University of Pretoria [South Africa]

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).


Volume: Volume 32 (2024), Issue 1
Published on: January 16, 2023
Accepted on: December 28, 2022
Submitted on: December 28, 2022
Keywords: Two-step nilpotent Lie group,sub-Riemannian structure,isometries,MSC 2020: 17B40, 53C17, 22E25.,[MATH]Mathematics [math]

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