Sub-riemannian (2, 3, 5, 6)-structures

Yu. L. Sachkov ; E. F. Sachkova

Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 73-78.

Résumé

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.

Détail

Keywords: sub-Riemannian geometry, Carnot algebras, Carnot groups, left-invariant sub-Riemannian structures.

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