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arXiv · 2609.11665

A vanishing result for harmonic $(n-1,1)$-forms

Matthias Wink
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Abstract

We prove that every primitive harmonic $(n-1,1)$-form of a closed K\"ahler manifold of complex dimension $n$ vanishes provided its K\"ahler curvature operator is $\frac{n^2-n+2}{2}$-positive if $n \geq 4$, respectively $\frac{7}{2}$-positive if $n=3$. As a consequence, a closed K\"ahler manifold of complex dimension $n \geq 3$ with $3$-positive K\"ahler curvature operator is a real cohomology complex projective space.

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Matthias Wink. 2026-09-10. A vanishing result for harmonic $(n-1,1)$-forms. https://arxiv.org/abs/2609.11665

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