论文标题
喷气空间中的度量线
Metric lines in Jet Space
论文作者
论文摘要
给定一个亚riemannian歧管，一个相关的问题是：什么是度量线（真实线的等距嵌入）？ The space of $k$-jets of a real function of one real variable $x$, denoted by $J^k(\mathbb{R},\mathbb{R})$, admits the structure of a Carnot group, as every Carnot group $J^k(\mathbb{R},\mathbb{R})$ is a sub-Riemannian Manifold.这项工作致力于在$ j^k（\ mathbb {r}，\ mathbb {r}）$中对公制行的分类提供部分结果。证明主要定理的方法是使用中间体$ 3 $二维的次 - riemannian Space $ \ Mathbb {r}^{3}^{3} _f $位于组$ j^k之间J^k（\ Mathbb {r}，\ Mathbb {r}） / [J^k（\ Mathbb {r}，\ Mathbb {r}），j^k（\ Mathbb {r {r}，\ Mathbb {r}）] $。
Given a sub-Riemannian manifold, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of $k$-jets of a real function of one real variable $x$, denoted by $J^k(\mathbb{R},\mathbb{R})$, admits the structure of a Carnot group, as every Carnot group $J^k(\mathbb{R},\mathbb{R})$ is a sub-Riemannian Manifold. This work is devoted to provide a partial result about the classification of the metric lines in $J^k(\mathbb{R},\mathbb{R})$. The method to prove the main Theorems is to use an intermediate $3$-dimensional sub-Riemannian space $\mathbb{R}^{3}_F$ lying between the group $J^k(\mathbb{R},\mathbb{R})$ and the Euclidean space $\mathbb{R}^{2} \simeq J^k(\mathbb{R},\mathbb{R}) / [J^k(\mathbb{R},\mathbb{R}),J^k(\mathbb{R},\mathbb{R})]$.
