Orthogonal almost complex structure and its Nijenhuis tensor
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913706889183232 |
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| author | Tang, Zizhou Yan, Wenjiao |
| author_facet | Tang, Zizhou Yan, Wenjiao |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal almost complex structure and its Nijenhuis tensor Tang, Zizhou Yan, Wenjiao Differential Geometry Complex Variables 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. |
| title | Orthogonal almost complex structure and its Nijenhuis tensor |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2401.14213 |