S.-S. Chern's study of almost-complex structures on the six-sphere

2014/05/14 by Bryant, Robert L.
#53A55 #53B15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1405.3405

Abstract

In 2003, S.-s. Chern began a study of almost-complex structures on the 6-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group G₂. While he did not solve the (currently still open) problem of determining whether there exists an integrable almost-complex structure on the 6-sphere, he did prove a significant identity that resolves the question for an interesting class of almost-complex structures on the 6-sphere.

Related

• The complex structure on the six dimensional sphere
• On the topology of the space of almost complex structures on the six sphere
• The Non-Existent Complex 6-Sphere
• Almost Complex Structure on S²ⁿ
• About generalized complex structures on \mathbb S⁶