Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-trivial $m$-quasi-Einstein metrics on simple Lie groups   We call a metric $m$-quasi-Einstein if $Ric_X^m$, which replaces a gradient
of a smooth function $f$ by a vector field $X$ in $m$-Bakry-Emery Ricci tensor,
is a constant multiple of the metric tensor. It is a generalization of Einstein
metrics which contains Ricci solitons. In this paper, we focus on
left-invariant metrics on simple Lie groups. First, we prove that $X$ is a
left-invariant Killing vector field if the metric on a compact simple Lie group
is $m$-quasi-Einstein. Then we show that every compact simple Lie group admits
non-trivial $m$-quasi-Einstein metrics except $SU(3)$, $E_8$ and $G_2$, and
most of them admit infinitely many metrics. Naturally, the study on
$m$-quasi-Einstein metrics can be extended to pseudo-Riemannian case. And we
prove that every compact simple Lie group admits non-trivial $m$-quasi-Einstein
Lorentzian metrics and most of them admit infinitely many metrics. Finally, we
prove that some non-compact simple Lie groups admit infinitely many non-trivial
$m$-quasi-Einstein Lorentzian metrics.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an