Geodesic
Sub-riemannian (2, 3, 5, 6)-structures
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 73-78

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We describe all Carnot algebras with growth vector (2, 3, 5, 6), their normal forms, an invariant that separates them, and a change of basis that transforms such an algebra into a normal form. For each normal form, Casimir functions and symplectic foliations on the Lie coalgebra are computed. An invariant and normal forms of left-invariant (2, 3, 5, 6)-distributions are described. A classification, up to isometries, of all left-invariant sub-Riemannian structures on (2, 3, 5, 6)-Carnot groups is obtained.
Keywords: sub-Riemannian geometry, Carnot algebras, Carnot groups, left-invariant sub-Riemannian structures. 
@article{DANMA_2021_496_a15,
     author = {Yu. L. Sachkov and E. F. Sachkova},
     title = {Sub-riemannian (2, 3, 5, 6)-structures},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {73--78},
     publisher = {mathdoc},
     volume = {496},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_496_a15/}
}
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Yu. L. Sachkov; E. F. Sachkova. Sub-riemannian (2, 3, 5, 6)-structures. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 73-78. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a15/