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

Chen, Qiang; Zhu, Meng

doi:10.1090/S0002-9939-2012-11648-X

On rigidity of gradient Kähler-Ricci solitons with harmonic Bochner tensor
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by Qiang Chen and Meng Zhu PDF

Proc. Amer. Math. Soc. 140 (2012), 4017-4025 Request permission

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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