2006/08/02 by Jianwei Zhou, Zhou, Jianwei
Mathematics · Physics and Astronomy · #14M15 #53C15 #53C27 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:14M15 #msc:53C15 #msc:53C27
paper · pdf · doi:10.48550/arxiv.math/0608052
11 pages
openalex publication_date 2006/08/02 · arxiv created 2006/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we use Clifford algebra and the spinor calculus to study the complex structures on Euclidean space R8 and the spheres S4,S6. By the spin representation of G(2,8)⊂ Spin(8) we show that the Grassmann manifold G(2,8) can be looked as the set of orthogonal complex structures on R8. In this way, we show that G(2,8) and CP3 can be looked as twistor spaces of S6 and S4 respectively. Then we show that there is no almost complex structure on sphere S4 and there is no orthogonal complex structure on the sphere S6.