具有非负双截曲率的紧致Vaisman流形与l.c.K.流形
Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature
- University of California, San Diego（加州大学圣地亚哥分校）
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AI总结：
本文研究紧致Vaisman与l.c.K.流形在非负双截曲率下的结构，推广Mok均匀化定理并给出三分法分类。
AI中文摘要：
本文研究具有非负双截曲率的紧致Vaisman流形与l.c.K.流形的结构。我们的第一个主要结果（见定理1.3）是紧致Vaisman流形的均匀化定理，将Mok在Kähler情形的均匀化定理（见[Mok88]）推广到Vaisman流形。我们的第二个结果（见定理1.6）给出了具有非负Chern双截曲率的紧致l.c.K.流形的结构三分法：其底复流形要么 admits 一个Kähler度量，要么 admits 一个Vaisman度量，要么其万有覆盖共形等价于一个不完备Kähler流形与一个正维复欧氏空间的乘积。
英文摘要：
We study the structure of compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature in this paper. Our first main result (cf. Theorem 1.3) is a uniformization theorem for compact Vaisman manifolds, extending Mok's uniformization theorem in the Kähler setting (cf. [Mok88]). Our second result (cf. Theorem 1.6) gives a structural trichotomy for compact l.c.K. manifolds with nonnegative Chern bisectional curvature: the underlying complex manifold admits a Kähler metric, admits a Vaisman metric, or its universal cover is conformally equivalent to the product of an incomplete Kähler manifold and a positive-dimensional complex Euclidean space.
