Non-trivial m-quasi-Einstein metrics on quadratic Lie groups

2014/01/09 by Zhiqi Chen, Ke Liang, Chen, Zhiqi +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1401.1922

openalex publication_date 2014/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Naturally reductive metrics and Einstein metrics on compact Lie groups

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