On the geometry of gradient Einstein-type manifolds

Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli and Marco Rigoli

Vol. 286 (2017), No. 1, 39–67

DOI: 10.2140/pjm.2017.286.39

Abstract

In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\left(M,g\right)$, 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.

Keywords

Einstein-type manifolds, Ricci solitons, Rigidity results

Mathematical Subject Classification 2010

Primary: 53C20, 53C25, 53A55

Milestones

Received: 17 February 2016

Revised: 12 April 2016

Accepted: 14 July 2016

Published: 9 December 2016