Compact kähler manifolds of nonnegative holomorphic bisectional curvature

1986 ◽  
pp. 90-103 ◽  
Author(s):  
Ngaiming Mok
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Holomorphic Bisectional Curvature

On complete noncompact Kähler manifolds with positive bisectional curvature

2003 ◽  
Vol 327 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Bing-Long Chen ◽  
Xi-Ping Zhu
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Positive Bisectional Curvature

scholarly journals Ricci flow on compact Kähler manifolds of positive bisectional curvature

2003 ◽  
Vol 337 (12) ◽  
pp. 781-784 ◽  
Author(s):  
Huai-Dong Cao ◽  
Bing-Long Chen ◽  
Xi-Ping Zhu
Keyword(s):  
Ricci Flow ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Positive Bisectional Curvature

scholarly journals Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles

2020 ◽  
Author(s):  
Ping Li ◽  
Fangyang Zheng
Keyword(s):  
Chern Class ◽  
Vector Bundles ◽  
Euler Number ◽  
Type Inequality ◽  
Chern Number ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Chern Numbers ◽  
Nef Vector Bundles

Abstract This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our 1st main result is a family of sharp Chern class inequalities. Among them the 1st one is a variant of a classical result and the equality case of the 2nd one is a characterization of hypersurfaces. The 2nd main result is a Chern number inequality on it, which includes a reverse Miyaoka–Yau-type inequality. The 3rd main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

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