The complex structure on the six dimensional sphere
Differential Geometry
2024-10-08 v6 Algebraic Geometry
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.
Cite
@article{arxiv.1509.02300,
title = {The complex structure on the six dimensional sphere},
author = {Gabor Etesi},
journal= {arXiv preprint arXiv:1509.02300},
year = {2024}
}
Comments
18 pages, no figures, LaTeX; the previous erroneous claim that S^6 as a complex manifold embeds into G_2 as a complex manifold removed without effecting the proof; comments are welcome