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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On rigidity of gradient Kähler-Ricci solitons with harmonic Bochner tensor


Authors: Qiang Chen and Meng Zhu
Journal: Proc. Amer. Math. Soc. 140 (2012), 4017-4025
MSC (2010): Primary 53C44, 53C55
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.


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Additional 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
Email: mez206@lehigh.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11648-X
PII: S 0002-9939(2012)11648-X
Keywords: Kähler-Ricci soliton, Bochner tensor, rigidity
Received by editor(s): May 12, 2011
Published electronically: March 28, 2012
Communicated by: Lei Ni
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.