TitoloGeneralized quasi-Einstein manifolds with harmonic Weyl tensor
Autore/iCatino, G.
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PubblicatoMath. Z., 271 (2012), no. 3-4, 751-756
AbstractIn this paper we introduce the notion of generalized quasi--Einstein manifold, which generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a warped product with (n?1)--dimensional Einstein fibers. In particular, this implies a local characterization for locally conformally flat gradient Ricci almost solitons, similar to the one proved for gradient Ricci solitons.