TY - JOUR

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

AU - Liu, Gang

N1 - Funding Information:
The author was partially supported by NSF Grant DMS 1406593.
Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

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.

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U2 - 10.1007/s00208-017-1536-0

DO - 10.1007/s00208-017-1536-0

M3 - Article

AN - SCOPUS:85016091872

SN - 0025-5831

VL - 370

SP - 649

EP - 667

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1-2

ER -