On the geometry of gradient einstein-type manifolds

By G. Catino, P. Mastrolia, D. Monticelli, M. Rigoli. 2014

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f8b472a30306b07b990c3cd24e29ad8f050ba918