On rigidity of gradient k?hler-ricci solitons with harmonic bochner tensor

摘要

In this paper, we prove that complete gradient steady K?hler-Ricci solitons with harmonic Bochner tensor are necessarily K?hler-Ricci flat, i.e., Calabi-Yau, and that complete gradient shrinking (or expanding) K?hler-Ricci solitons with harmonic Bochner tensor must be isometric to a quotient of N ~k ×C ~(n-k), where N is a K?hler-Einstein manifold with positive (or negative) scalar curvature.