The complex structure on the six dimensional sphere

2015/09/08 by Gábor Etesi, Etesi, Gabor
Mathematics · Physics and Astronomy · #32J25 #53C56 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #Primary: 32J17 #Secondary: 22C05

paper · pdf · doi:10.48550/arxiv.1509.02300

openalex publication_date 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Proof of existence of a complex structure on the six-sphere, followed by an explicit computation of its underlying integrable almost complex tensor by the aid of inner automorphisms of the octonions, is exhibited. Both are elementary and self-contained however the size and complexity of the emerging almost complex tensor field on the six-sphere is perplexing.

Related

• The Non-Existent Complex 6-Sphere
• S.-S. Chern's study of almost-complex structures on the six-sphere
• About generalized complex structures on \mathbb S⁶
• A note on Kirchhoff's theorem for almost complex spheres I
• Curvature, integrability, and the six sphere