On rigidity of gradient Kähler-Ricci solitons with harmonic Bochner tensor
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- by Qiang Chen and Meng Zhu
- Proc. Amer. Math. Soc. 140 (2012), 4017-4025
- DOI: https://doi.org/10.1090/S0002-9939-2012-11648-X
- Published electronically: March 28, 2012
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Abstract:
In this paper, we prove that complete gradient steady Kähler-Ricci solitons with harmonic Bochner tensor are necessarily Kähler-Ricci flat, i.e., Calabi-Yau, and that complete gradient shrinking (or expanding) Kähler-Ricci solitons with harmonic Bochner tensor must be isometric to a quotient of $N^k\times \mathbb {C}^{n-k}$, where $N$ is a Kähler-Einstein manifold with positive (or negative) scalar curvature.References
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Bibliographic Information
- Qiang Chen
- Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
- Email: qic208@lehigh.edu
- Meng Zhu
- Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
- MR Author ID: 888985
- Email: mez206@lehigh.edu
- Received by editor(s): May 12, 2011
- Published electronically: March 28, 2012
- Communicated by: Lei Ni
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4017-4025
- MSC (2010): Primary 53C44, 53C55
- DOI: https://doi.org/10.1090/S0002-9939-2012-11648-X
- MathSciNet review: 2944741