On rigidity of gradient kähler-ricci solitons with harmonic bochner tensor

Qiang Chen; Meng Zhu

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

On rigidity of gradient kähler-ricci solitons with harmonic bochner tensor

Qiang Chen^*
, Meng Zhu

^*此作品的通讯作者

Lehigh University

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

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

源语言	英语
页（从-至）	4017-4025
页数	9
期刊	Proceedings of the American Mathematical Society
卷	140
期	11
DOI	https://doi.org/10.1090/S0002-9939-2012-11648-X
出版状态	已出版 - 2012
已对外发布	是

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

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

KW - Bochner tensor

KW - Kähler-Ricci soliton

KW - Rigidity

UR - https://www.scopus.com/pages/publications/84863963826

U2 - 10.1090/S0002-9939-2012-11648-X

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On rigidity of gradient kähler-ricci solitons with harmonic bochner tensor

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