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^*

^*Corresponding author for this work

Northwestern University

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

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	649-667
Number of pages	19
Journal	Mathematische Annalen
Volume	370
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-017-1536-0
State	Published - 1 Feb 2018
Externally published	Yes

Access to Document

10.1007/s00208-017-1536-0

Cite this

@article{0ea992da0b9a462daeded00950abc247,

title = "On the tangent cone of K{\"a}hler manifolds with Ricci curvature lower bound",

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.",

author = "Gang Liu",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag Berlin Heidelberg.",

year = "2018",

month = feb,

day = "1",

doi = "10.1007/s00208-017-1536-0",

language = "英语",

volume = "370",

pages = "649--667",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - On the tangent cone of Kähler manifolds with Ricci curvature lower bound

AU - Liu, Gang

PY - 2018/2/1

Y1 - 2018/2/1

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85016091872

U2 - 10.1007/s00208-017-1536-0

DO - 10.1007/s00208-017-1536-0

M3 - 文章

AN - SCOPUS:85016091872

SN - 0025-5831

VL - 370

SP - 649

EP - 667

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1-2

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this