Compact Kähler manifolds with nonpositive bisectional curvature

Gang Liu

doi:10.1007/s00039-014-0290-7

Compact Kähler manifolds with nonpositive bisectional curvature

Gang Liu^*

^*此作品的通讯作者

University of California at Berkeley

科研成果: 期刊稿件 › 文章 › 同行评审

12 引用（Scopus）

摘要

Let (Mⁿ, g) be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold N^k with c₁ < 0. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.

源语言	英语
页（从-至）	1591-1607
页数	17
期刊	Geometric and Functional Analysis
卷	24
期	5
DOI	https://doi.org/10.1007/s00039-014-0290-7
出版状态	已出版 - 1 9月 2014
已对外发布	是

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abstract = "Let (Mn, g) be a compact K{\"a}hler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact K{\"a}hler manifold Nk with c1 < 0. This confirms a conjecture of Yau. As a corollary, for any compact K{\"a}hler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.",

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AB - Let (Mn, g) be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold Nk with c1 < 0. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.

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Compact Kähler manifolds with nonpositive bisectional curvature

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