English

Rigidity of Quasi-Einstein Metrics

Differential Geometry 2010-12-16 v1 Metric Geometry

Abstract

We call a metric quasi-Einstein if the mm-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the construction of the warped product Einstein metrics. We study properties of quasi-Einstein metrics and prove several rigidity results. We also give a splitting theorem for some K\"ahler quasi-Einstein metrics.

Keywords

Cite

@article{arxiv.0805.3132,
  title  = {Rigidity of Quasi-Einstein Metrics},
  author = {Jeffrey Case and Yujen Shu and Guofang Wei},
  journal= {arXiv preprint arXiv:0805.3132},
  year   = {2010}
}

Comments

10 pages

R2 v1 2026-06-21T10:42:36.274Z