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

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

2011-05-05

arxiv.org/abs/1105.1152v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we prove that complete gradient steady K\"ahler-Ricci solitons with harmonic Bochner tensor are necessarily K\"ahler-Ricci flat, i.e., Calabi-Yau, and that complete gradient shrinking (or expanding) K\"ahler-Ricci solitons with harmonic Bochner tensor must be isometric to a quotient of $N^k\times \mathbb{C}^{n-k}$, where $N$ is a K\"ahler-Einstein manifold with positive (or negative) scalar curvature.

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