Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indefinite almost paracontact metric manifolds   In this paper we introduce the concept of $(\varepsilon)$-almost paracontact
manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds.
Several examples are presented. Some typical identities for curvature tensor
and Ricci tensor of $(\varepsilon)$-para Sasakian manifolds are obtained. We
prove that if a semi-Riemannian manifold is one of flat, proper recurrent or
proper Ricci-recurrent, then it can not admit an $(\varepsilon)$-para Sasakian
structure. We show that, for an $(\varepsilon)$-para Sasakian manifold, the
conditions of being symmetric, semi-symmetric or of constant sectional
curvature are all identical. It is shown that a symmetric spacelike (resp.
timelike) $(\varepsilon)$-para Sasakian manifold $M^{n}$ is locally isometric
to a pseudohyperbolic space $H_{\nu}^{n}(1)$ (resp. pseudosphere
$S_{\nu}^{n}(1)$). In last, it is proved that for an $(\varepsilon)$-para
Sasakian manifold, the conditions of being Ricci-semisymmetric, Ricci-symmetric
and Einstein are all identical.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph