On the geometry of gradient Einstein-type manifolds

Abstract

In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\varrg$, unifying various particular cases recently studied in the literature, such as gradient Ricci solitons, Yamabe solitons and quasi-Einstein manifolds. We show that these general structures can be locally classified when the Bach tensor is null. In particular, we extend a recent result of Cao and Chen.

References in corpus (4)

• Evolution of the Weyl Tensor under the Ricci Flow
• Bach-flat gradient steady Ricci solitons
• On a classification of the quasi Yamabe gradient solitons
• Rigidity of gradient Einstein shrinkers

Cited by in corpus (3)

• Homogeneous Ricci almost solitons
• Berger curvature decomposition, Weitzenböck formula, and canonical metrics on four-manifolds
• Bach-flat noncompact steady quasi-Einstein manifolds