Rigidity of Quasi-Einstein Metrics

Abstract

We call a metric quasi-Einstein if the $m$-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 Kähler quasi-Einstein metrics.

10 pages

References in corpus (1)

• New Inhomogeneous Einstein Metrics on Sphere Bundles Over Einstein-Kahler Manifolds

Cited by in corpus (2)

• Smooth metric measure spaces, quasi-Einstein metrics, and tractors
• Warped product Einstein metrics over spaces with constant scalar curvature