Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contact Pairs   We introduce a new geometric structure on differentiable manifolds. A
\textit{Contact} \textit{Pair}on a manifold $M$ is a pair $(\alpha,\eta) $ of
Pfaffian forms of constant classes $2k+1$ and $2h+1$ respectively such that
$\alpha\wedge d\alpha^{k}\wedge\eta\wedge d\eta^{h}$ is a volume form. Both
forms have a characteristic foliation whose leaves are contact manifolds. These
foliations are transverse and complementary. Further differential objects are
associated to Contact Pairs: two commuting Reeb vector fields, Legendrian
curves on $M$ and two Lie brackets on $\mathcal{C}^{\infty}(M) $. We give a
local model and several existence theorems on nilpotent Lie groups,
nilmanifolds, bundles over the circle and principal torus bundles.

7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys