Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Almost Paracontact Structures on Affine Hypersurfaces   Let $\widetilde{J}$ be the canonical para-complex structure on
$\mathbb{R}^{2n+2}\simeq\widetilde{\mathbb{C}}^{n+1}$. We study real affine
hypersurfaces $f\colon M\rightarrow \widetilde{\mathbb{C}}^{n+1}$ with a
$\widetilde{J}$-tangent transversal vector field. Such vector field induces in
a natural way an almost paracontact structure ${(\varphi,\xi,\eta)}$ on $M$ as
well as the affine connection $\nabla$. In this paper we give the
classification of hypersurfaces with the property that $\varphi$ or $\eta$ is
parallel relative to the connection $\nabla$. Moreover, we show that if
$\nabla\varphi=0$ (respectively $\nabla\eta=0$) then around each point of $M$
there exists a parallel almost paracontact structure. Results we illustrate
with some examples.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con