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تسجيل مستخدم جديدNon-trivial $m$-quasi-Einstein metrics on quadratic Lie groups
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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.
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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
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