On the tangent cone of Kähler manifolds with Ricci curvature lower bound

Gang Liu

doi:10.1007/s00208-017-1536-0

On the tangent cone of Kähler manifolds with Ricci curvature lower bound

Gang Liu^*

^*此作品的通讯作者

Northwestern University

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

Let X be the Gromov–Hausdorff limit of a sequence of pointed complete Kähler manifolds (Min,pi) satisfying Ric(M_i) ≥ - (n- 1) and the volume is noncollapsed. We prove that, there exists a Lie group isomorphic to R, acting isometrically, on the tangent cone at each point of X. Moreover, the action is locally free on the cross section. This generalizes the metric cone theorem of Cheeger–Colding to the Kähler case. We also discuss some applications to complete Kähler manifolds with nonnegative bisectional curvature.

源语言	英语
页（从-至）	649-667
页数	19
期刊	Mathematische Annalen
卷	370
期	1-2
DOI	https://doi.org/10.1007/s00208-017-1536-0
出版状态	已出版 - 1 2月 2018
已对外发布	是

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abstract = "Let X be the Gromov–Hausdorff limit of a sequence of pointed complete K{\"a}hler manifolds (Min,pi) satisfying Ric(Mi) ≥ - (n- 1) and the volume is noncollapsed. We prove that, there exists a Lie group isomorphic to R, acting isometrically, on the tangent cone at each point of X. Moreover, the action is locally free on the cross section. This generalizes the metric cone theorem of Cheeger–Colding to the K{\"a}hler case. We also discuss some applications to complete K{\"a}hler manifolds with nonnegative bisectional curvature.",

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AB - Let X be the Gromov–Hausdorff limit of a sequence of pointed complete Kähler manifolds (Min,pi) satisfying Ric(Mi) ≥ - (n- 1) and the volume is noncollapsed. We prove that, there exists a Lie group isomorphic to R, acting isometrically, on the tangent cone at each point of X. Moreover, the action is locally free on the cross section. This generalizes the metric cone theorem of Cheeger–Colding to the Kähler case. We also discuss some applications to complete Kähler manifolds with nonnegative bisectional curvature.

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ER -

On the tangent cone of Kähler manifolds with Ricci curvature lower bound

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