PreprintCC BY 4.0arXiv
Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature
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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BibTeX
@misc{li2026compact,
title = {{Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature}},
author = {Jiangtao Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25880},
eprint = {2609.25880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25880},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Compact Vaisman and l.c.K. manifolds with nonnegative bisectional curvature
AU - Jiangtao Li
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25880
UR - https://arxiv.org/abs/2609.25880
AB - 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.
ER -