Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Ricci curvature of metric structures on $\mathfrak{g}$-manifolds   We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with
particular attention paid to higher dimensional abelian Lie algebra case. The
relations between Ricci curvature of the manifold and the Ricci curvature of
the transverse manifold of the characteristic foliation are investigated. In
particular, sufficient conditions are found under which the
${\mathfrak{g}}$-manifold can be a Ricci soliton or a gradient Ricci soliton.
Finally, we obtain a amazing (non-existence) higher dimensional generalization
of the Boyer-Galicki theorem on Einstein K-manifolds for a special class of
abelian ${\mathfrak{g}}$-manifolds.

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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph