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arXiv · 2609.25880

Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature

Jiangtao Li
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Abstract

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.

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Jiangtao Li. 2026-09-22. Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature. https://arxiv.org/abs/2609.25880

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