Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Foliations with Transversal Quaternionic Structures   We consider manifolds equipped with a foliation $\cal F$ of codimension $4q$,
and an almost quaternionic structure $Q$ on the transversal bundle of ${\cal
F}$. After discussing conditions of projectability and integrability of $Q$, we
study the transversal twistor space $Z{\cal F}$ which, by definition, consists
of the $Q$-compatible almost complex structures. We show that $Z{\cal F}$ can
be endowed with a lifted foliation ${\hat {\cal F}}$ and two natural almost
complex structures $J_1$, $J_2$ on the transversal bundle of $\hat{\cal F}$. We
establish the conditions which ensure the projectability of $J_1$ and $J_2$,
and the integrability of $J_{1}$ ($J_{2}$ is never integrable).

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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci