The Kähler-Ricci flow on Kähler manifolds with 2-non-negative traceless bisectional curvature operator

Xiuxiong Chen; Haozhao Li

doi:10.1007/s11401-007-0294-9

The Kähler-Ricci flow on Kähler manifolds with 2-non-negative traceless bisectional curvature operator

Xiuxiong Chen
, Haozhao Li

Mathematics

Peking University

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

4 Scopus citations

Abstract

The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Kähler-Ricci flow. The positivity of Ricci curvature is also preserved along the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Kähler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.

Original language	English
Pages (from-to)	543-556
Number of pages	14
Journal	Chinese Annals of Mathematics. Series B
Volume	29
Issue number	5
DOIs	https://doi.org/10.1007/s11401-007-0294-9
State	Published - Sep 2008

Keywords

2-non-negative bisectional curvature
Kähler-Ricci flow

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10.1007/s11401-007-0294-9

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abstract = "The authors show that the 2-non-negative traceless bisectional curvature is preserved along the K{\"a}hler-Ricci flow. The positivity of Ricci curvature is also preserved along the K{\"a}hler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the K{\"a}hler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a K{\"a}hler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.",

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AU - Chen, Xiuxiong

AU - Li, Haozhao

PY - 2008/9

Y1 - 2008/9

N2 - The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Kähler-Ricci flow. The positivity of Ricci curvature is also preserved along the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Kähler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.

AB - The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Kähler-Ricci flow. The positivity of Ricci curvature is also preserved along the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Kähler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.

KW - 2-non-negative bisectional curvature

KW - Kähler-Ricci flow

UR - https://www.scopus.com/pages/publications/53549098228

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DO - 10.1007/s11401-007-0294-9

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AN - SCOPUS:53549098228

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JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 5

ER -

The Kähler-Ricci flow on Kähler manifolds with 2-non-negative traceless bisectional curvature operator

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Keywords

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