In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold.M; g/, 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.
On the geometry of gradient einstein-type manifolds / G. Catino, P. Mastrolia, D.D. Monticelli, M. Rigoli. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - 286:1(2017), pp. 39-67.
On the geometry of gradient einstein-type manifolds
P. MastroliaSecondo
;M. RigoliUltimo
2017
Abstract
In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold.M; g/, 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.
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