# On the geometry of gradient Einstein-type manifolds

created by catino on 14 Feb 2014
modified on 28 Jan 2017

[BibTeX]

Published Paper

Inserted: 14 feb 2014
Last Updated: 28 jan 2017

Journal: Pac. J. Math.
Volume: 286
Number: 1
Pages: 39-67
Year: 2017

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 \cite{CaoChen}.