# Generalized quasi-Einstein manifolds with harmonic Weyl tensor

created by catino on 17 Feb 2011
modified on 14 Jul 2012

[BibTeX]

Published Paper

Inserted: 17 feb 2011
Last Updated: 14 jul 2012

Journal: Math. Z.
Volume: 271
Number: 3-4
Pages: 751-756
Year: 2012

Abstract:

In 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.