Carnot Algebras and Sub-Riemannian Structures with Growth Vector (2,$\,$3,$\,$5,$\,$6)

Yu. L. Sachkov ; E. F. Sachkova

Informatics and Automation, Optimal Control and Differential Games, Tome 315 (2021), pp. 237-246.

Résumé

We describe all Carnot algebras with growth vector $(2,3,5,6)$, their normal forms, an invariant that distinguishes them, and a basis change that reduces such an algebra to a normal form. For every normal form, we calculate the Casimir functions and symplectic foliations on the Lie coalgebra. We describe the invariant and the normal forms of left-invariant $(2,3,5,6)$-distributions. We also obtain a classification of all left-invariant sub-Riemannian structures on $(2,3,5,6)$-Carnot groups up to isometry and present models of these structures.

Détail

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

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