论文标题
亚里曼尼亚的几何形状中的均质大地测量学
Homogeneous geodesics in sub-Riemannian geometry
论文作者
论文摘要
我们研究了亚riemannian歧管的均质测量学，即正常的测量学，是异构体的单参数亚组的轨道。我们获得了一个测量的标准，即在其初始动量方面具有同质性。我们证明，任何弱接合性的次摩曼尼亚均质均匀空间都是大地轨道，这意味着所有测量学都是同质的。我们讨论了一些大地轨道次摩曼尼亚歧管的示例。特别是，我们表明地球轨道carnot组只是步骤$ 1 $和$ 2 $的组。最后，我们至少存在一种均匀的大地测量，我们的情况很广。
We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum. We prove that any weakly commutative sub-Riemannian homogeneous space is geodesic orbit, that means all geodesics are homogeneous. We discuss some examples of geodesic orbit sub-Riemannian manifolds. In particular, we show that geodesic orbit Carnot groups are only groups of step $1$ and $2$. Finally, we get a broad condition for existence of at least one homogeneous geodesic.
