Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature. (English) Zbl 1444.32022
Authors’ abstract: In this paper we prove a gap theorem for Kähler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author [Invent. Math. 189, No. 3, 737–761 (2012; Zbl 1253.32009)]. We also prove a Liouville theorem for plurisubharmonic functions on such a manifold, which generalizes a previous result of the first author and L.-F. Tam [J. Differ. Geom. 64, No. 3, 457–524 (2003; Zbl 1088.32013)] and complements a recent result of G. Liu [Duke Math. J. 165, No. 15, 2899–2919 (2016; Zbl 1356.53070)].
Reviewer: Mihai Putinar (Santa Barbara)
MSC:
| 32Q15 | Kähler manifolds |
| 32U05 | Plurisubharmonic functions and generalizations |
| 32Q10 | Positive curvature complex manifolds |
References:
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