Abstract

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.

中文翻译：

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次黎曼（2，3，5，6）-结构

摘要

我们用生长向量（2、3、5、6），它们的正常形式，将它们分开的不变式以及将这种代数转换成正常形式的基础变化来描述所有Carnot代数。对于每个范式，都可以计算出Lie代数上的卡西米尔函数和辛叶面。描述了左不变（2、3、5、6）分布的不变形式和正态形式。获得了对（2、3、5、6）-卡诺组上所有左不变亚黎曼结构的直至同构的分类。