Results Concerning Almost Complex Structures on the Six-Sphere

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Wilson, S.O.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209538
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Results Concerning Almost Complex Structures on the Six-Sphere / S.O. Wilson // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 12 назв. — англ.

For the standard metric on the six-dimensional sphere, with Levi-Civita connection ∇, we show there is no almost complex structure J such that ∇XJ and ∇JXJ commute for every X, nor is there any integrable J such that ∇JXJ = J∇XJ for every X. The latter statement generalizes a previously known result...