Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solvable extensions of negative Ricci curvature of filiform Lie groups   We give necessary and sufficient conditions of the existence of a
left-invariant metric of strictly negative Ricci curvature on a solvable Lie
group the nilradical of whose Lie algebra $\mathfrak{g}$ is a filiform Lie
algebra $\mathfrak{n}$. It turns out that such a metric always exists, except
for in the two cases, when $\mathfrak{n}$ is one of the algebras of rank two,
$L_n$ or $Q_n$, and $\mathfrak{g}$ is a one-dimensional extension of
$\mathfrak{n}$, in which cases the conditions are given in terms of certain
linear inequalities for the eigenvalues of the extension derivation.

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The categories of this paper are: cs
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
19
The categories of this paper are: eess