论文标题
卡诺组的喷气空间
Jet spaces on Carnot groups
论文作者
论文摘要
$ \ Mathbb r^n $上的喷气空间已被证明具有分层谎言组的规范结构（也称为Carnot组）。我们在适应水平分化的分层谎言基团上构建喷气空间，并表明这些喷气空间本身是分层的谎言组。此外，我们表明这些喷气空间支持接触图的延长理论，尤其是Bäcklund型定理。这些结果的副产品是一个嵌入定理，表明步骤$ s+1 $的每个分层的谎言组都可以嵌入到零件$ s $的分层谎言组上。
Jet spaces on $\mathbb R^n$ have been shown to have a canonical structure of stratified Lie groups (also known as Carnot groups). We construct jet spaces over stratified Lie groups adapted to horizontal differentiation and show that these jet spaces are themselves stratified Lie groups. Furthermore, we show that these jet spaces support a prolongation theory for contact maps, and in particular, a Bäcklund type theorem holds. A byproduct of these results is an embedding theorem that shows that every stratified Lie group of step $s+1$ can be embedded in a jet space over a stratified Lie group of step $s$.
