Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The foliated structure of contact metric $(\kappa,\mu)$-spaces   In this paper we study the foliated structure of a contact metric
$(\kappa,\mu)$-space. In particular, using the theory of Legendre foliations,
we give a geometric interpretation to the Boeckx's classification of contact
metric $(\kappa,\mu)$-spaces and we find necessary conditions for a contact
manifold to admit a compatible contact metric $(\kappa,\mu)$-structure. Finally
we prove that any contact metric $(\kappa,\mu)$-space $M$ whose Boeckx
invariant $I_M$ is different from $\pm 1$ admits a compatible Sasakian or
Tanaka-Webster parallel structure according to the circumstance that $|I_M|>1$
or $|I_M|<1$, respectively.

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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin