Generalized quasi-Einstein manifolds with harmonic Weyl tensor

By G. Catino. Mathematische Zeitschrift, 2010

158 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/04851c61e85edf4c9fc101bd2b8502efe56993e5

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In Applied Mathematics

1. A. Barros
2. E. Ribeiro
3. Xiuxiong Chen
4. Yuanqi Wang
5. Robert J. Berman
6. G'abor Sz'ekelyhidi
7. Jeffrey Streets
8. S. Brendle

In Astronomy and Astrophysics

1. A. Barros
2. E. Ribeiro
3. Xiuxiong Chen
4. Yuanqi Wang
5. Jeffrey Streets
6. Jacob Sturm
7. Duong H. Phong
8. Robert J. Berman

In Geometry and Topology

1. A. Barros
2. E. Ribeiro
3. Xiuxiong Chen
4. Yuanqi Wang
5. Robert J. Berman
6. G'abor Sz'ekelyhidi
7. B. Weinkove
8. Jeffrey Streets

Citations in the corpus

• On Four-Dimensional Anti-self-dual Gradient Ricci Solitons (2011, methodology): “For more references on Ricci solitons and quasi-Einstein metrics with vanishing Weyl tensor, see [10] and [11].”
• Characterizations and integral formulae for generalized m-quasi-Einstein metrics (2012, background): “[11] Catino, G.: Generalized quasi-Einstein manifolds with harmonic weyl tensor.”