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

2011/05/05 by Qiang Chen, Meng Zhu, Chen, Qiang +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1105.1152

minor errors corrected

arxiv created 2012/08/13 · arxiv updated 2012/08/14

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 Nk× ℂn-k, where N is a Kähler-Einstein manifold with positive (or negative) scalar curvature.

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