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

Gang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)649-667
Number of pages19
JournalMathematische Annalen
Volume370
Issue number1-2
DOIs
StatePublished - Feb 1 2018

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On the tangent cone of Kähler manifolds with Ricci curvature lower bound'. Together they form a unique fingerprint.

  • Cite this