About generalized complex structures on \mathbb S⁶

2024/05/09 by Fernando Etayo, Etayo, Fernando, Pablo Gómez-Nicolás +2
Mathematics · Physics and Astronomy · #53C15 #53D18 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2405.05681

openalex publication_date 2024/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence of generalized complex structures on the six-dimensional sphere \mathbb S⁶. We work with the generalized tangent bundle \mathbb T\mathbb S⁶→ \mathbb S⁶ 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 S⁶ from its usual nearly Kähler structure inherited from the octonions product.

Related

• S⁶ and the geometry of nearly Kähler 6-manifolds
• The complex structure on the six dimensional sphere
• Grassmann Manifold G(2,8) and Complex Structure on S⁶
• S.-S. Chern's study of almost-complex structures on the six-sphere
• Group Actions on S⁶ and complex structures on P₃