TY - JOUR
T1 - On the tangent cone of Kähler manifolds with Ricci curvature lower bound
AU - Liu, Gang
N1 - 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.
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 -