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arXiv · 1402.3453

On the geometry of gradient Einstein-type manifolds

Giovanni Catino·Paolo Mastrolia·Dario Monticelli·Marco Rigoli
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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.

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Giovanni Catino, Paolo Mastrolia, Dario Monticelli, Marco Rigoli. 2014-02-14. On the geometry of gradient Einstein-type manifolds. https://arxiv.org/abs/1402.3453

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