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A vanishing result for harmonic (n−1,1)-forms
Abstract
We prove that every primitive harmonic (n−1,1)-form of a closed Kähler manifold of complex dimension n vanishes provided its Kähler curvature operator is (n2−n+2)/2-positive if n ≥ 4, respectively 7/2-positive if n=3. As a consequence, a closed Kähler manifold of complex dimension n ≥ 3 with $3$-positive Kähler curvature operator is a real cohomology complex projective space.
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BibTeX
@misc{wink2026vanishing,
title = {{A vanishing result for harmonic $(n-1,1)$-forms}},
author = {Matthias Wink},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11665},
eprint = {2609.11665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11665},
}
RIS
TY - UNPB
TI - A vanishing result for harmonic (n−1,1)-forms
AU - Matthias Wink
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.11665
UR - https://arxiv.org/abs/2609.11665
AB - We prove that every primitive harmonic (n−1,1)-form of a closed Kähler manifold of complex dimension n vanishes provided its Kähler curvature operator is (n^2−n+2)/2-positive if n ≥ 4, respectively 7/2-positive if n=3. As a consequence, a closed Kähler manifold of complex dimension n ≥ 3 with $3$-positive Kähler curvature operator is a real cohomology complex projective space.
ER -