Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural Almost Hermitian Structures on Conformally Foliated
  4-Dimensional Lie Groups with Minimal Leaves   Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional
left-invariant, conformal foliation $\mathcal{F}$ with minimal leaves. Let $J$
be an almost Hermitian structure on $G$ adapted to the foliation $\mathcal{F}$.
The corresponding Lie algebra $\mathfrak{g}$ must then belong to one of 20
families $\mathfrak{g}_1,\dots,\mathfrak{g}_{20}$ according to S. Gudmundsson
and M. Svensson. We classify such structures $J$ which are almost K\"{a}hler
$(\mathcal{A}\mathcal{K})$, integrable $(\mathcal{I})$ or K\"{a}hler
$(\mathcal{K})$. Hereby, we construct 16 multi-dimensional almost K\"{a}hler
families, 18 integrable families and 11 K\"{a}hler families.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg