On the geometry of gradient Einstein-type manifolds
Differential Geometry
2017-04-25 v1
Abstract
In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold , 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
@article{arxiv.1402.3453,
title = {On the geometry of gradient Einstein-type manifolds},
author = {Giovanni Catino and Paolo Mastrolia and Dario Monticelli and Marco Rigoli},
journal= {arXiv preprint arXiv:1402.3453},
year = {2017}
}