arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1301.1306math.DGmath-phmath.MP
收藏

叶状向量丛与黎曼叶状

Foliated vector bundles and riemannian foliations

Paul Popescu, Marcela Popescu

备注：
6 pages
发表信息：
C. R. Acad. Sci. Paris, Ser. I 349 (2011) 445-449
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文的目的是证明下列条件中的每一个都等价于叶理${\cal F}$是黎曼的：1）$r$ -横向喷流束上的抬升叶理${\cal F}^{r}$对于$r\geq 1$是黎曼的; 2）切割${\cal J}_{0}^{r}$上的叶理${\cal F}_{0}^{r}$对于$r\geq 1 $是黎曼的和垂直精确的; 3）对于$r\geq 1$，在${\cal J}%_{0}^{r}E$上存在一个正容许的横拉格朗日量，即$r$ --叶理丛$% E\rightarrow M$的横割喷流丛。

英文摘要：

The purpose of this Note is to prove that each of the following conditions is equivalent to that of the foliation ${\cal F}$ is riemannian: 1) the lifted foliation ${\cal F}^{r}$ on the bundle of $r$-transverse jets is riemannian for an $r\geq 1$; 2) the foliation ${\cal F}_{0}^{r}$ on the slashed ${\cal J}_{0}^{r}$ is riemannian and vertically exact for an $r\geq 1 $; 3) there is a positively admissible transverse lagrangian on ${\cal J}%_{0}^{r}E$, the $r$-transverse slashed jet bundle of a foliated bundle $% E\rightarrow M$, for an $r\geq 1$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑