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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.14213 |
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Table of Contents:
- In this paper, we demonstrate that on an almost Hermitian manifold $(M^{2n}, J, ds^2)$, a 2-form $φ=S^*Φ$, the pulling back of the Kähler form $Φ$ on the twistor bundle over $M^{2n}$, is non-degenerate if the squared norm $|N|^2$ of the Nijenhuis tensor is less than $\frac{64}{5}$ when $n\geq 3$ or less than $16$ when $n=2$. As a corollary, there exists no orthogonal almost complex structure on the standard sphere $(S^6, ds_0^2)$ with $|N|^2<\frac{64}{5}$ everywhere.