Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Paracontact metric structures on the unit tangent sphere bundle   Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on
the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold
$(M,\langle,\rangle)$, we construct a family of paracontact metric structures.
We prove that this class of paracontact metric structures is invariant under
$\mathcal D$-homothetic deformations, and classify paraSasakian and paracontact
$(\kappa,\mu)$-spaces inside this class. We also present a way to build
paracontact $(\kappa,\mu)$-spaces from corresponding contact metric structures
on $T_1 M$.

28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph