A left-invariant sub-Riemannian problem on a free nilpotent Lie group of step 4 with two generators is considered. The structure of abnormal extremals is described. These extremals are shown to define an abnormal foliation of the annihilator of the square of the distribution, which is given by the intersections of this annihilator with the leaves of the symplectic foliation of the Lie coalgebra. The question of abnormal trajectories being strictly/nonstrictly abnormal is investigated, their projection onto a plane of the distribution are described, estimates for the corank are given and examples of nonsmooth trajectories are constructed.

Bibliography: 14 titles.

中文翻译：

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具有增长向量的亚黎曼问题中异常极值的结构

考虑具有两个生成器的步骤4的自由幂立李群上的左不变亚黎曼问题。描述了异常肢体的结构。这些极值显示出定义了分布平方的an灭者的异常叶状，这是由该an灭者与Lie coalgebra辛叶状化的叶子的交点给出的。研究了异常轨迹是严格/非严格异常的问题，描述了它们在分布平面上的投影，给出了对估计的估计，并构造了非平滑轨迹的示例。

参考书目：14种。