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On products of locally conformally Kähler manifolds
Abstract
We prove that no product of positive-dimensional compact complex manifolds admits a strict locally conformally Kähler (lcK) metric. This solves a long-standing conjecture in lcK geometry, previously established only under certain conditions.
Related
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BibTeX
@misc{stanciu2026products,
title = {{On products of locally conformally Kähler manifolds}},
author = {Miron Stanciu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05964},
eprint = {2609.05964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05964},
}
RIS
TY - UNPB
TI - On products of locally conformally Kähler manifolds
AU - Miron Stanciu
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05964
UR - https://arxiv.org/abs/2609.05964
AB - We prove that no product of positive-dimensional compact complex manifolds admits a strict locally conformally Kähler (lcK) metric. This solves a long-standing conjecture in lcK geometry, previously established only under certain conditions.
ER -