Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-naturally reductive Einstein metrics on $\mathrm{SO}(n)$   In this article, we prove that every compact simple Lie group $SO(n)$ for
$n\geq 10$ admits at least $2\left([\frac{n-1}{3}]-2\right)$ non-naturally
reductive left-invariant Einstein metrics.

3
The categories of this paper are: physics
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex