Grassmann Manifold G(2,8) and Complex Structure on $S^6$
| dc.creator | Zhou, Jianwei | |
| dc.date | 2006-08-02 | |
| dc.date | 2006-08-18 | |
| dc.date.accessioned | 2026-07-07T07:21:17Z | |
| dc.date.available | 2026-07-07T07:21:17Z | |
| dc.description | In this paper, we use Clifford algebra and the spinor calculus to study the complex structures on Euclidean space $R^8$ and the spheres $S^4,S^6$. By the spin representation of $G(2,8)\subset Spin(8)$ we show that the Grassmann manifold G(2,8) can be looked as the set of orthogonal complex structures on $R^8$. In this way, we show that G(2,8) and $CP^{3}$ can be looked as twistor spaces of $S^6$ and $S^4$ respectively. Then we show that there is no almost complex structure on sphere $S^4$ and there is no orthogonal complex structure on the sphere $S^6$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608052 | |
| dc.identifier | http://arxiv.org/abs/math/0608052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115252 | |
| dc.subject | Differential Geometry | |
| dc.subject | 14M15,53C15,53C27 | |
| dc.title | Grassmann Manifold G(2,8) and Complex Structure on $S^6$ | |
| dc.type | text |