Sub-Riemannian (2, 3, 5, 6)-Structures

Sub-Riemannian (2, 3, 5, 6)-Structures

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 inv...

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Veröffentlicht in:Doklady. Mathematics 2021, Vol.103 (1), p.61-65
Hauptverfasser: Sachkov, Yu. L., Sachkova, E. F.
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Canonical forms
Control Theory
Invariants
Mathematics
Mathematics and Statistics
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description 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.
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subjects Canonical forms
Control Theory
Invariants
Mathematics
Mathematics and Statistics
title Sub-Riemannian (2, 3, 5, 6)-Structures
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