Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher order transverse bundles and riemannian foliations   The purpose of this paper is to prove that each of the following conditions
is equivalent to that the foliation ${\cal F}$ is riemannian: 1) the lifted
foliation ${\cal F}^{r}$ on the $r$-transverse bundle $\nu ^{r}{\cal F}$ is
riemannian for an $r\geq 1$; 2) the foliation ${\cal F}_{0}^{r}$ on a slashed
$\nu_{\ast}^{r}{\cal F}$ is riemannian and vertically exact for an $r\geq 1$;
3) there is a positively admissible transverse lagrangian on a
$\nu_{\ast}^{r}{\cal F}$, for an $r\geq 1$. Analogous results have been proved
previously for normal jet vector bundles.

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ