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

^*Corresponding author for this work

Lehigh University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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

Original language	English
Pages (from-to)	4017-4025
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2012-11648-X
State	Published - 2012
Externally published	Yes

Keywords

Bochner tensor
Kähler-Ricci soliton
Rigidity

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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

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

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

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

Abstract

Keywords

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