%0 Journal Article
%T Non-trivial $m$-quasi-Einstein metrics on quadratic Lie groups
%A Zhiqi Chen
%A Ke Liang
%A Fahuai Yi
%J Mathematics
%D 2014
%I arXiv
%X We call a metric $m$-quasi-Einstein if $Ric_X^m$ (a modification of the $m$-Bakry-Emery Ricci tensor in terms of a suitable vector field $X$) 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 vector fields and left-invariant Riemannian metrics on quadratic Lie groups. First we prove that any left-invariant vector field $X$ such that the left-invariant Riemannian metric on a quadratic Lie group is $m$-quasi-Einstein is a Killing field. Then we construct infinitely many non-trivial $m$-quasi-Einstein metrics on solvable quadratic Lie groups $G(n)$ for $m$ finite.
%U http://arxiv.org/abs/1401.1922v2