Journal
MATHEMATISCHE ZEITSCHRIFT
Volume 271, Issue 3-4, Pages 751-756Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00209-011-0888-5
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Funding
- Italian project FIRB-IDEAS Analysis and Beyond
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In this paper we introduce the notion of generalized quasi-Einstein manifold that 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 that proved for gradient Ricci solitons.
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