# References on almost complex structures on spheres

I'm looking for a proof of that the only spheres with almost complex structure are $S^2$ and $S^6$. I've googled "almost complex structure sphere", but all I get is comments saying that "this fact is well-known".

Are there good write-ups on this topic? Thanks in advance.

• References are given at the beginning of Chapter VI of the book "Almost complex and complex structures" by C.C. Hsiung. It uses characteristic classes and cohomology operations to get obstructions. – BCnrd May 22 '10 at 6:42
• One must be careful with the last chapters of the book BCnrd mentioned, I think Dr. Bryant has said on this site that there is an error in them – user74900 Apr 29 '18 at 7:21