About generalized complex structures on $\mathbb S^6$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915402055942144 |
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| author | Etayo, Fernando Gómez-Nicolás, Pablo Santamaría, Rafael |
| author_facet | Etayo, Fernando Gómez-Nicolás, Pablo Santamaría, Rafael |
| contents | We study the existence of generalized complex structures on the six-dimensional sphere $\mathbb S^6$. We work with the generalized tangent bundle $\mathbb T\mathbb S^6\to \mathbb S^6$ and define the integrability of generalized geometric structures in terms of the Dorfman bracket. Specifically, we prove that there is not a direct way to induce a generalized complex structure on $\mathbb S^6$ from its usual nearly Kähler structure inherited from the octonions product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | About generalized complex structures on $\mathbb S^6$ Etayo, Fernando Gómez-Nicolás, Pablo Santamaría, Rafael Differential Geometry 53D18, 53C15 We study the existence of generalized complex structures on the six-dimensional sphere $\mathbb S^6$. We work with the generalized tangent bundle $\mathbb T\mathbb S^6\to \mathbb S^6$ and define the integrability of generalized geometric structures in terms of the Dorfman bracket. Specifically, we prove that there is not a direct way to induce a generalized complex structure on $\mathbb S^6$ from its usual nearly Kähler structure inherited from the octonions product. |
| title | About generalized complex structures on $\mathbb S^6$ |
| topic | Differential Geometry 53D18, 53C15 |
| url | https://arxiv.org/abs/2405.05681 |